TopCoder Statistics - Problem Statement

Problem Statement

You are in charge of preparing the next big hit: a show called the calamari game.

For this show you have created a variation of a children's game. You call it "red light, green light, blue light". Your version of this game looks as follows:

There are some participants. Initially, each participant is some number of steps away from the goal line. You are given these distances in the int[] steps.

The game is played in turns. Each turn looks as follows:

Each participant turns on one of the three lights on their helmet: red, green, or blue.
A scary mechanical doll with a machine gun will choose one of the colors. The players with the chosen color are allowed to take one step towards the goal line. All other players are immediately eliminated from the game.

The players win when at least one of them reaches the goal line. The doll wins when everyone gets eliminated.

Given the starting locations of all players, determine whether a cooperating group of players has a winning strategy. If they don't, return {-1}. If they do, find one winning set of choices the players should make in the first turn of the game. Return a int[] with one element for each player (in the order in which they are given in the input). Each element of the return value should be 0, 1, or 2. These values represent the three different light colors each player can choose from.

Definition

Class:: RedGreenBlueLight
Method:: move
Parameters:: int[]
Returns:: int[]
Method signature:: int[] move(int[] steps)
(be sure your method is public)

Constraints

steps will contain between 1 and 1000 elements, inclusive.
Each element of steps will be between 1 and 999,999,999, inclusive.

Examples

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

Returns: {0, 2, 2, 1, 0, 2, 0, 0, 2, 1 }

As long as these players don't make the mistake of just choosing one or two colors only, they will win the game after its first round.
{11, 11, 11, 11, 11, 11, 11, 11, 11, 11}

Returns: {-1 }

The doll can guarantee to eliminate at least one player per round, and if it does so, this bunch of players doesn't stand a chance.
{7, 8, 9, 7, 7, 8, 9, 8, 7, 9, 7, 7, 8, 8}

Returns: {-1 }

The doll can use better strategies than the one described in the previous example. For example, whenever there are 14 players as in this example, the doll can easily make sure that at most four of them will reach the next turn.
{1, 2, 3, 4, 5, 6, 7, 999888777, 2, 3, 4, 5, 2, 3, 2, 9, 1, 7, 2, 3, 4, 5, 6, 7, 15}

Returns: {2, 0, 1, 1, 0, 2, 1, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 2, 1 }
{1}

Returns: {-1 }
{1,1}

Returns: {-1 }
{1,1,1}

Returns: {0, 1, 2 }
{1,2,2,1}

Returns: {-1 }
{1,2,2,1,2}

Returns: {0, 2, 2, 1, 2 }
{1,2,2,987654321,1,2}

Returns: {0, 2, 2, 2, 1, 2 }
{2,2,2,2,2,3,2,3,2,2}

Returns: {-1 }
{2,2,2,2,2,3,2,3,2,2,3}

Returns: {0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 2 }
{1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4}

Returns: {-1 }
{1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4}

Returns: {0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,44,444,44444}

Returns: {0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{6, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 7, 7, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 6, 7, 6, 7, 7, 7, 7, 6, 6, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 7, 7, 6, 7, 6, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 7, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 6, 7, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 7, 7, 6, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 7, 7, 6, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 7, 7, 6, 7, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 7, 6, 7, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 6, 7, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 7, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 7, 6, 7, 7, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

Returns: {0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{7, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 6, 6, 7, 6, 6, 8, 6, 7, 7, 6, 7, 6, 6, 6, 6, 7, 7, 6, 6, 6, 7, 7, 7, 6, 6, 7, 6, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 6, 7, 6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 6, 7, 6, 6, 7, 7, 7, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 6, 7, 6, 6, 7, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 7, 6, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 6, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 6, 7, 6, 7, 6, 6, 7, 7, 7, 7, 6, 7, 6, 6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 6, 7, 6, 6, 7, 7, 7, 7, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 7, 6, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 7, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 6, 7, 6, 7, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 7, 6, 6, 6, 7, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 7, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 6, 6, 6, 7, 6, 7, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 6, 6, 7, 7, 7, 6, 7, 7, 7, 7, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 7, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 6, 6, 7, 7, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 7, 7, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 6, 7, 7, 7, 6, 7, 6, 6, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 7, 6, 7, 6, 6, 7, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7}

Returns: {-1 }
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Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
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Returns: {-1 }
{8, 7, 8, 11, 11, 6, 6, 9, 6, 10, 9, 9, 10, 8, 11, 6, 10, 7, 4, 9, 11, 12, 8, 9, 7, 13, 8, 9, 5, 9, 9, 12, 10, 14, 15, 7, 8, 9, 14, 8, 10, 6, 10, 11, 8, 9, 11, 15, 6, 7, 11, 10, 10, 9, 6, 11, 11, 8, 7, 3, 9, 10, 9, 14, 16, 8, 8, 6, 3, 7, 11, 10, 9, 9, 9, 9, 7, 6, 9, 7, 7, 6, 11, 7, 8, 6, 7, 10, 7, 11, 9, 9, 10, 8, 10, 9, 7, 9, 15, 12, 6, 9, 7, 6, 5, 12, 7, 6, 12, 12, 7, 10, 8, 5, 9, 9, 9, 9, 12, 11, 6, 8, 7, 11, 7, 16, 11, 9, 12, 5, 7, 5, 7, 12, 9, 12, 11, 9, 171067, 8, 4, 10, 11, 14, 6, 7, 9, 8, 9, 9, 7, 5, 10, 2, 14, 9, 5, 6, 15, 7, 12, 10, 9, 13, 8, 7, 8, 11, 13, 11, 7, 7, 5, 7, 9, 9, 12, 8, 12, 11, 9, 8, 12, 6, 8, 9, 15, 11, 8, 12, 11, 10, 11, 8, 7, 8, 28299, 11, 15, 11, 14, 8, 11, 11, 8, 10, 9, 9, 9, 14, 7, 10, 11, 9, 10, 10, 10, 8, 8, 7, 8, 6, 8, 9, 6, 7, 8, 10, 9, 8, 6, 8, 9, 13, 10, 8, 7, 11, 9, 9, 11, 11, 8, 9, 8, 7, 8, 9, 5, 10, 8, 8, 9, 6, 10, 9, 13, 6, 9, 97177264, 11, 10, 11, 9, 8, 11, 11, 9, 11, 21430533, 14, 7, 7, 5, 9, 9, 9, 11, 9, 9, 6, 6, 9, 4, 13, 11, 14, 9, 9, 9, 12, 13, 6, 9, 9, 8, 8, 3, 6, 8, 7, 10, 3, 11, 6, 9, 8, 11, 8, 6, 9, 9, 5, 8, 9, 7, 9, 10, 7, 281984, 7, 9, 7, 6, 9, 10, 11, 6, 16, 12, 15, 9, 6, 11, 10, 6, 8, 5, 9, 12, 10, 10, 5, 7, 11, 7, 16, 12, 8, 6, 8, 9, 10, 6, 8, 6, 6, 9, 7, 12, 7, 10, 8, 7, 9, 9, 12, 8, 12, 6, 6, 7, 7, 7, 7, 10, 8, 9, 14, 13, 8, 6, 7, 8, 6, 11, 8, 11, 16, 7, 7, 15, 11, 9, 8, 7, 11, 8, 6, 8, 12, 9, 8, 8, 9, 7, 13, 9, 10, 10, 12, 10, 8, 8, 7, 6, 7, 7, 2, 9, 5, 8, 8, 6, 5, 9, 8, 10, 11, 10, 8, 5, 13, 15, 11, 10, 11, 16, 15, 8, 8, 8, 12, 11, 8, 5, 15, 10, 7, 10, 9, 16, 10, 9, 11, 9, 9, 8, 16, 8, 7, 12, 11, 8, 8, 9, 6, 7, 8, 5, 9, 8, 8, 6, 5, 12, 11, 10, 9, 9, 15, 8, 12, 11, 9, 9, 16, 8, 11, 8, 7, 9, 9, 6, 6, 9, 14, 6, 9, 9, 7, 10, 10, 6, 7, 11, 7, 11, 12, 10, 10, 10, 11, 7, 10, 8, 6, 10, 6, 8, 8, 9, 7, 9, 8, 9, 12, 5, 7, 8, 9, 8, 11, 5, 14, 7, 8, 8, 14, 10, 11, 9, 13, 6, 8, 10, 11, 11, 11, 9, 6, 12, 13, 11, 5, 10, 9, 13, 3, 8, 6, 13, 6, 5, 12, 13, 16, 8, 15, 11, 7, 11, 11, 10, 13, 5, 12, 7, 10, 11, 10, 7, 9, 7, 10, 9, 9, 6, 11, 15, 7, 9, 7, 8, 5, 7, 6, 9, 11, 7, 10, 11, 11, 8, 10, 7, 9, 8, 10, 4, 15, 10, 8, 9, 8, 7, 8, 8, 4, 7, 9, 11, 7, 12, 9, 11, 9, 8, 7, 9, 7, 16, 12, 8, 10, 6, 10, 15, 8, 12, 8, 6, 4, 9, 6, 9, 11, 6, 10, 9, 7, 16, 10, 4, 10, 8, 8, 6, 6, 8, 7, 10, 9, 7, 10, 13, 9, 8, 6, 7, 8, 7, 11, 13, 10, 11, 6, 11, 9, 9, 7, 7, 5992963, 7, 15, 7, 11, 7, 8, 9, 8, 8, 9, 11, 9, 11, 12, 7, 9, 9, 7, 9, 6, 12, 10, 7, 8, 9, 9, 10, 12, 12, 9, 12, 11, 7, 6, 11, 8, 11, 6, 8, 8, 7, 10, 9, 8, 8, 11, 8, 7, 5, 13, 9, 8, 9, 12, 13, 8, 10, 10, 8, 8, 7, 8, 8, 9, 8, 8, 11, 10, 9, 7, 8, 5, 4, 10, 8, 8, 7, 10, 12, 15, 6, 11, 14, 7, 6, 12, 10, 14, 106171979, 5, 10, 10, 6, 10, 9, 9, 4, 11, 10, 11, 6, 8, 7, 9, 10, 8, 8, 8, 11, 6, 6, 11, 11, 9, 8, 11, 11, 8, 15, 11, 5, 11, 11, 12, 8, 10, 11, 6, 10, 9, 11, 9, 8, 10, 5, 3, 5, 7, 10, 10, 12, 11, 9, 9, 9, 7, 16, 12, 6, 8, 11, 12, 9, 10, 6, 9, 10, 10, 9, 16, 7, 11, 10, 8, 6, 6, 8, 9, 5, 9, 7, 9, 12, 13, 13, 7, 8, 7, 13, 8, 9, 5, 9, 5, 7, 6, 8, 9, 10, 7, 8, 11, 6, 11, 11, 13, 10, 11, 8, 12, 15, 5, 7, 15, 8, 11, 9, 8, 8, 10, 5, 9, 8, 9, 5, 13, 7, 8, 3, 7, 16, 6, 15, 5, 14, 6, 10, 9, 9, 7, 10, 9, 10, 12, 11, 5, 10, 7, 6, 8, 7, 10, 12, 6, 12, 13, 9, 10, 10, 8, 7, 8, 6, 11, 7, 10, 9, 8, 11, 12, 8, 7, 9, 10, 12, 8, 9, 10, 11, 10, 9, 9, 13, 11, 11, 14, 14, 3, 11}

Returns: {-1 }
{9, 12, 12, 7, 9, 9, 8, 4, 10, 7, 9, 6, 3316, 7, 1525200, 9, 8, 9, 10, 8, 9, 519698317, 7, 7, 4, 12, 10, 7, 10, 9, 7, 7, 8, 10, 12, 9, 10, 7, 9, 6, 4, 6, 8, 9, 7, 7, 8, 8, 6, 7, 10, 10, 10, 7, 9, 8, 5, 8, 8, 7, 6, 10, 5, 12, 7, 9, 8, 9, 6, 6, 9, 8, 9, 9, 11, 7, 9, 8, 11, 7, 6, 7, 4, 5, 11, 10, 5, 9, 7, 8, 8, 9, 9, 8, 7, 84407205, 5, 3048681, 12, 8, 6, 9, 8, 8, 11, 8, 9, 8, 9, 9, 12, 9, 5, 9, 10, 8, 8, 8, 9, 10, 5, 8, 6, 6, 8, 9, 6, 8, 9, 8, 70270782, 6, 10, 7, 9, 8, 8, 9, 10, 7, 6, 12, 5, 8, 9, 8, 10, 7, 127934901, 7, 7, 8, 8, 8, 9, 4, 9, 4, 6, 7, 9, 9, 6, 9, 6, 8, 6, 9, 12, 10, 7, 10, 6, 5, 5, 13, 8, 11, 6, 9, 8, 8, 11, 8, 6, 5, 8, 9, 6, 10, 10, 11, 9, 11, 9, 11, 11, 7, 6, 11, 9, 7, 9, 8, 7, 6, 7, 7, 5, 5, 7, 5, 10, 7, 8, 9, 11, 8, 7, 11, 8, 3, 11, 12, 9, 5, 8, 8, 6, 10, 6, 6, 7, 10, 9, 6, 6, 8, 8, 4, 8, 6, 6, 9, 9, 12, 10, 8, 6, 9, 6, 10, 10, 7, 5, 6, 10, 7, 8, 5, 8, 5, 6, 8, 10, 7, 7, 5, 9, 6, 7, 8, 9, 7, 6, 3040, 8, 9, 9, 7, 9, 7, 7, 12, 8, 8, 9, 9, 9, 5, 9, 7, 8, 11, 10, 7, 5, 9, 8, 6, 7, 10, 9, 11, 6, 8831216, 11, 8, 6, 8, 6, 9, 9, 8, 133901, 326205, 9, 9, 9, 6, 10, 7, 6, 8, 940236, 8, 7, 7, 27649, 8, 7, 8, 10, 7, 9, 9, 8, 10, 11, 6, 5, 9, 10, 4, 11, 8, 11, 8, 10, 8, 8, 10, 10, 9, 6, 10, 8, 6, 9, 5, 8, 6, 10, 7, 10, 7, 6, 8, 8, 7, 6, 9, 4, 2429579, 9, 5, 8, 7, 7, 9, 8, 9, 7, 9, 8, 12, 11, 7, 9, 5, 7, 8, 10, 8, 8, 8, 8, 10, 8, 10, 9, 8, 8, 9, 8, 12, 7, 9, 6, 11, 10, 6, 10, 9, 8, 6, 8, 5, 5, 5, 5, 5, 8, 7, 12, 7, 9, 8, 9, 9, 8, 11, 7, 9, 10, 10, 9, 8, 11, 8, 8, 8, 8, 11, 8, 7, 8, 7, 7, 9, 8, 7, 8, 7, 8, 7, 6, 6, 8, 8, 7, 6, 7, 10, 8, 8, 8, 7, 7, 2043848, 9, 8, 6, 7, 4, 8, 6, 4, 7, 9, 4, 12, 8, 7, 9, 11, 8, 8, 8, 4, 9, 9, 5, 10, 5, 10, 11, 9, 7, 10, 32734, 13, 6, 8, 6, 7, 5, 9, 9, 9, 9, 10, 7, 7, 6, 10, 9, 8, 10, 8, 9, 8, 10, 10, 7, 8, 9, 4, 10, 11, 309240190, 5, 6, 9, 6, 6, 11, 7, 7, 5, 10, 4, 6, 5, 6, 4, 9, 9, 8, 7, 7, 8, 9, 6, 9, 5, 470103342, 5, 5, 8, 9, 9, 7, 6, 22099489, 11, 5, 8, 6, 12, 8, 8, 9, 8, 7, 5, 10, 4, 10, 6, 4, 7, 9, 8, 8, 8, 7, 7, 8, 10, 8, 9, 8, 13905052, 9, 8, 9, 7, 9, 9, 10, 10, 4, 5, 9, 10, 7, 8, 7, 10, 10, 7, 8, 2739, 8, 8, 4, 10, 8, 6, 8, 7, 8, 8, 7, 10, 6, 7, 10, 9, 13597, 6, 8, 8, 6, 8, 10, 9, 6, 5, 10, 8, 12, 10, 5, 7, 6, 7, 5, 6, 7, 12, 9, 8, 8, 8, 7, 9, 10, 7, 6, 9, 8, 7, 9, 6, 4703097, 6, 6, 7, 7, 9, 5, 7, 2968487, 5, 8, 8, 8, 7, 9, 8, 8, 7, 8, 7, 9, 9, 8, 11, 7, 7, 7, 10, 10, 9, 6, 7, 8, 7, 7, 9, 8, 6, 9, 4, 8, 8, 6, 9, 4, 7, 5, 8, 9, 7, 10, 7, 4, 8, 7, 9, 9, 7, 79659, 8, 5, 10, 8, 6, 9, 6, 9, 9, 8, 10, 2053164, 8, 12, 9, 7, 8, 9, 8, 8, 9, 8, 8, 9, 9, 6, 6, 9, 11, 9, 10, 7, 12, 9, 9, 9, 6, 1543471, 11, 8, 8, 8, 8, 8, 10, 9, 6, 9, 7, 9, 53962, 9, 6, 9, 8, 8, 7, 7, 6, 6, 4148888, 11, 8, 7, 7, 289087862, 10, 7, 10, 11, 7, 7, 7, 1950, 6, 10, 7, 6, 9, 9, 11, 8, 7, 8, 8, 12916, 8, 5, 8, 8, 8, 9, 8, 8, 8, 12, 5, 6, 5, 9, 6, 9, 8, 9, 9, 4, 8, 9, 7, 8, 6, 10, 7, 9, 7, 8, 10, 9, 5, 9, 5, 10, 11, 9, 9448979, 8, 5, 9, 9, 9, 7, 6, 88985862, 8, 5, 9, 8, 7, 3, 8, 10, 5, 6, 8, 9, 9, 8, 10, 146265271, 9, 7, 6, 8, 7, 30595296, 6, 11, 5, 9, 6, 9, 8, 6, 10, 5, 6, 6845094, 9, 7, 9, 8, 7, 7, 10, 5, 6, 7, 30132, 8, 10, 7, 6, 9, 6, 9, 8, 10, 10, 8, 10, 9, 5, 13, 8, 9, 9, 6, 7298509, 8, 5, 6, 4, 8, 11, 11, 5, 7, 11, 9, 7, 10, 9, 4, 4, 5, 8, 8, 7, 4, 6, 7, 10, 9, 9, 5, 5, 9, 6, 5, 12, 8, 4, 9, 10, 6, 10, 8, 8, 9, 11, 6, 7, 8, 8, 9, 7, 4, 11, 7, 10, 7, 9, 8, 10, 10, 10436, 10, 9, 9, 7, 10, 9, 6, 9, 9, 7, 5, 9}

Returns: {-1 }
{6, 12, 497003322, 11, 9, 8, 7, 11, 8, 7, 13, 8, 11, 209272714, 9, 10, 7, 10, 7, 9, 8, 7, 10, 7, 1031649, 8, 10, 13, 8, 7, 11, 11, 10, 12, 8, 9, 7, 13, 9, 5, 8, 12, 10, 9, 9, 7, 7, 7, 4, 6, 9, 7999075, 6, 10, 10, 9, 6, 8, 7, 7, 9, 9, 9, 6, 7, 6, 12, 9, 13, 12, 11, 13, 7, 4, 7, 12, 10, 10, 6, 8, 6, 9, 5, 7, 7, 11, 14, 9, 12, 5, 7, 10, 11, 8, 12, 13, 5, 9, 9, 7, 10, 6, 9, 11, 9, 11, 11, 10, 9, 8, 11, 7, 12, 10, 7, 6, 5, 8, 10, 9, 9, 7, 8, 8, 11, 6, 7, 14, 46642229, 5, 8, 6, 30813, 3, 10, 13, 13, 7, 9, 9, 7, 338256, 7, 7, 10, 7, 8, 8, 6, 11, 10, 14, 4, 11, 9, 12, 11, 10, 11, 3, 6, 5, 7, 12, 7, 9, 8, 9, 9, 7, 11, 8, 10, 268295782, 10, 12, 7, 8, 13, 6, 13, 8, 11, 10, 9, 8, 7, 8, 6, 13, 8, 513652246, 6, 10, 9, 8, 11, 7, 14, 7, 8, 9, 6, 13, 8, 8, 8, 27983626, 12, 6, 12, 8, 8, 9, 11, 10, 9, 12, 6, 9, 9, 12, 9, 7, 14603193, 8, 10, 258243735, 8, 7, 11, 10, 7, 8, 8, 8, 5, 7, 9, 10, 8, 8, 1802, 9, 9, 11, 8, 9, 9, 9, 13, 10, 8, 10, 9, 8, 13, 12, 11, 8, 8, 10, 11, 11, 5, 7, 5, 11, 8, 3, 8, 10, 4, 9, 10, 9, 8, 13, 9, 8, 8, 9, 8, 8, 10, 11, 15, 34247, 13, 10, 4, 8, 9, 11, 9, 11, 1324, 11, 8, 9, 10, 10, 9, 7, 4, 11, 8, 11, 9, 8, 12, 13, 8, 16356992, 8, 8, 8, 13, 9, 7, 6, 12, 7, 8, 11, 8, 10, 10, 12, 9, 13, 12, 6, 8, 11, 8, 3, 9, 12, 9, 8, 4, 9, 11, 8, 13, 4, 10, 7, 11, 8, 10, 7, 9, 9, 7, 7, 74733427, 12, 11, 9, 4, 6, 9, 8, 6, 7, 8, 13, 232543001, 3, 11, 5, 4, 12, 8, 9, 10, 12, 8, 7, 1023226, 9, 12, 7, 6, 7, 8, 6, 11, 7, 3399, 7, 6, 11, 5, 6, 5, 10, 12, 11, 11, 9, 7, 11, 8, 12, 12, 5, 10, 10, 9, 12, 7, 13, 6, 9, 8, 11, 7, 8, 10, 8, 13, 7, 10, 8, 11, 7, 7, 11, 6, 11, 10, 4, 9, 7, 9, 9, 11, 7, 4, 11, 5, 11, 8, 10, 9, 11, 9, 6, 106723489, 9, 12, 8, 13, 8, 6, 3, 12, 10, 7, 7, 6, 7, 6, 11, 6, 8, 4, 8, 7, 8, 8, 7, 6, 11, 10, 13, 7, 9, 10, 6, 10, 6, 5, 10, 6, 9, 11, 3, 12, 7, 6, 6, 11, 11, 6, 7, 11, 11, 10, 7, 8, 11, 5, 11, 10, 8, 10, 8, 8, 11, 12, 5, 8, 4, 7, 10, 5, 10, 8, 12, 7, 1506, 11, 10, 12, 9, 10, 4, 11, 10, 8, 11, 10, 13, 4, 6, 6, 7, 10, 9, 9, 3, 8, 13, 8, 12, 11, 7, 11, 10, 7, 6, 12, 11, 10, 467257, 7, 6, 9, 5, 6, 10, 7, 10, 13, 7, 10, 6, 11, 10, 7, 12, 10, 6, 14346358, 11, 13, 10, 6, 7, 13, 11, 10, 10, 8, 12, 8, 9, 10, 8, 2615093, 5, 10, 7, 8, 5, 11, 13, 8, 8, 11, 10, 11, 9, 7, 10, 10, 10, 9, 11, 12, 10, 7, 5, 6, 392685, 11, 5, 14, 12, 11, 7, 4, 5, 4, 9, 8, 3706, 8, 11, 10, 5, 7, 11, 11, 9, 11, 12, 4, 9, 10, 7, 11, 13, 7, 8, 9, 9, 9, 9, 12, 9, 9, 13, 11, 9, 10, 6, 4, 8617, 12, 10, 8, 11, 9, 10, 9, 12, 10, 9, 7, 13, 9, 9, 6, 7, 10, 14, 9, 7, 9, 8, 13, 9, 9, 12, 9, 5, 7, 9, 8, 9, 13, 13, 9, 6, 8, 9, 12, 11, 10, 13, 8, 7, 6, 10, 11, 8, 8, 13, 8, 15, 11, 14, 8, 10, 12, 5, 10, 9, 12, 12, 10, 7, 11, 9, 10, 7, 9, 8, 8, 5, 9, 6, 14, 10, 3775317, 12, 7, 11, 7, 8, 7, 7, 9, 10, 11, 10, 10, 11, 7, 5, 16576099, 6, 8, 7, 12, 13, 11, 13, 11, 5, 1496, 7, 11, 12, 8, 7, 11, 6, 8, 8, 8, 4207, 6, 7, 7, 7, 10, 7, 9, 10, 9, 13, 13, 8, 41397949, 7, 11, 8, 6, 9, 11, 6, 10, 6, 11, 10, 9, 4, 11, 5, 9, 11, 11, 62238565, 5, 10, 10, 8, 10, 7, 10, 6, 12, 10, 5, 8335, 11, 10, 7, 10, 10, 7, 10, 6, 8, 10, 10, 7, 10, 10, 9, 11, 7, 8, 10, 8, 12, 15, 8, 9, 9, 11, 8, 9, 5, 11, 9, 13, 15, 10, 11, 8, 8, 7, 8, 9, 6, 10, 1356155, 14, 10, 6, 9, 12, 9, 13, 11, 10, 12, 9, 12, 6, 13, 8, 9, 5, 9, 6, 6, 7, 7, 11, 10, 9, 11, 9, 7, 11, 11, 9, 11, 3, 6, 10, 10, 12, 11, 9, 6, 15, 12, 8, 13, 11, 15, 10, 10, 10, 7, 8, 10, 9, 9, 11, 11, 11, 8, 11, 10, 11, 8, 12, 5, 7, 8, 11, 8, 4, 11, 8, 13, 8, 9, 12, 7, 4, 10, 7, 7, 12, 5, 10, 4, 11, 8, 12, 798767, 11, 13, 13, 12, 8, 9, 10, 7, 12, 10, 8, 9, 12, 7, 10, 9, 8, 7, 11, 4, 9, 6, 8, 11, 8, 7, 5, 9, 11, 14, 10, 5, 6, 7, 11, 10, 6, 12, 10, 10, 6, 8, 10, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{5, 9, 10, 7, 12, 9, 10, 11, 8, 12, 8, 11, 9, 8, 12, 19, 5, 9, 11, 10, 14, 9, 11, 13, 9, 10, 9, 12, 8, 11, 11, 9, 14, 11, 15, 12, 7, 10, 12, 11, 8, 4, 17, 12, 10, 5, 9, 12, 13, 13, 11, 6, 19, 12, 10, 11, 11, 10, 7, 4, 16, 7, 11, 9, 7, 11, 8, 12, 7, 3, 7, 11, 9, 10, 12, 7, 8, 9, 11, 8, 9, 11, 9, 9, 11, 15, 12, 7, 8, 5, 19, 15, 11, 7, 8, 19, 10, 7, 7, 5, 11, 2, 12, 9, 12, 12, 14, 14, 10, 6, 10, 13, 10, 8, 16, 19, 5, 8, 7, 6, 12, 11, 8, 7, 19, 8, 7, 12, 13, 8, 10, 5, 8, 9, 3, 11, 13, 8, 9, 8, 7, 6, 7, 13, 6, 10, 10, 8, 8, 9, 7, 11, 14, 18, 18, 10, 9, 18, 7, 7, 12, 9, 9, 10, 7, 9, 10, 10, 7, 11, 8, 20, 9, 8, 11, 3, 8, 8, 8, 17, 8, 18, 9, 6, 11, 10, 12, 5663880, 5, 10, 9, 6, 8, 18, 14, 7, 4, 17, 9, 10, 9, 8, 5, 12, 13, 7, 3, 8, 9, 11, 13, 6, 6, 19, 8, 13, 8, 12, 17, 9, 19, 9, 11, 11, 8, 8, 13, 8, 11, 9, 9, 10, 11, 13, 16, 12, 11, 14, 10, 9, 8, 7, 7, 16, 11, 7, 7, 9, 13, 16, 7, 11, 7, 9, 9, 13, 8, 9, 9, 8, 8, 9, 9, 12, 11, 10, 7, 10, 8, 9, 13, 8, 9, 8, 7, 8, 16, 10, 11, 12, 12, 6, 10, 9, 18, 9, 10, 10, 8, 7, 11, 9, 11, 9, 7, 12, 14, 12, 9, 8, 12, 7, 17, 11, 16, 14, 6, 11, 10, 10, 7, 7, 15, 11, 4, 16, 12, 10, 6, 7, 15, 8, 11, 6, 7, 8, 13, 11, 12, 11, 12, 21, 12, 5, 7, 5, 14, 7, 6, 18, 9, 11, 12, 11, 11, 7, 9, 9, 9, 9, 2, 8, 10, 18, 10, 9, 10, 8, 5, 9, 6, 8, 9, 6, 15, 20, 11, 10, 10, 8, 9, 10, 14, 9, 14, 9, 9, 12, 9, 13, 11, 13, 9, 10, 20, 12, 9, 8, 5, 10, 11, 8, 19, 7, 15, 11, 10, 10, 10, 13, 15, 11, 18, 10, 8, 12, 9, 11, 15, 11, 7, 10, 8, 8, 12, 12, 13, 12, 10, 8, 16, 7, 17, 9, 10, 7, 9, 8, 5, 6, 7, 10, 12, 8, 9, 15, 9, 12, 14, 6, 10, 10, 10, 9, 9, 10, 7, 8, 9, 11, 8, 10, 18, 7, 8, 11, 7, 6, 6, 19, 9, 9, 6, 10, 9, 11, 9, 11, 9, 8, 10, 10, 9, 8, 12, 8, 7, 107233880, 7, 7, 12, 12, 10, 7, 9, 12, 12, 19, 15, 6, 3, 8, 11, 10, 16, 16, 9, 7, 11, 10, 16, 13, 14, 7, 12, 10, 13, 18, 18, 13, 6, 19, 10, 15, 8, 11, 10, 7, 12, 19, 7, 10, 7, 7, 12, 12, 11, 11, 11, 13, 15, 10, 12, 10, 6, 12, 11, 17, 17, 8, 7, 11, 10, 11, 10, 11, 6, 9, 12, 8, 9, 12, 14, 11, 8, 10, 9, 7, 7, 8, 10, 10, 13, 5, 16, 17, 17, 11, 12, 8, 12, 10, 6, 14, 7, 15, 10, 10, 10, 9, 9, 11, 10, 11, 17, 12, 8, 10, 18, 7, 13, 10, 9, 7, 8, 10, 13, 1713729, 19, 8, 18, 8, 7, 11, 13, 9, 12, 12, 10, 7, 9, 6, 7, 17, 7, 5, 13, 7, 10, 18, 6, 2, 11, 7, 8, 12, 9, 11, 11, 9, 6, 8, 13, 13, 7, 8, 7, 11, 10, 12, 9, 12, 9, 9, 9, 14, 12, 9, 11, 9, 13, 7, 9, 7, 8, 5, 11, 13, 9, 17, 21, 7, 9, 13, 6, 8, 7, 18, 10, 8, 12, 9, 12, 6, 8, 10, 11, 8, 121796, 16, 10, 9, 4, 9, 13, 10, 11, 11, 19, 18, 15, 6, 11, 17, 9, 8, 8, 8, 12, 10, 10, 10, 9, 15, 6524, 8, 7, 7, 8, 8, 16, 7, 8, 14, 12, 7, 7, 10, 11, 8, 13, 12, 9, 11, 9, 9, 7, 5, 7, 6, 8, 12, 11, 9, 18, 6, 11, 8, 18, 11, 10, 14, 9, 11, 3, 6, 6, 7, 7, 10, 10, 8, 6, 8, 8, 10, 8, 12, 16, 7, 13, 9, 1485531, 11, 9, 11, 8, 7, 13, 6, 10, 13, 9, 7, 18, 7, 11, 15, 5, 6, 11, 10, 6, 11, 17, 19, 12, 10, 10, 11, 7, 11, 11, 6, 7, 17, 6, 13, 16, 19, 11, 12, 7, 9, 17, 12, 13, 9, 12, 11, 19, 17, 7, 12, 16, 6, 12, 17, 7, 11, 11, 7, 10, 11, 9, 7, 12, 9, 5, 13, 10, 10, 6, 10, 9, 11, 8, 9, 6, 10, 7, 13, 9, 11, 8, 5, 11, 7, 3, 13, 19, 13, 8, 8, 20, 9, 7, 9, 10, 13, 17, 18, 8, 9, 13, 15, 17, 13, 6, 9, 9, 18, 11, 17, 13, 14, 17, 8, 9, 8, 11, 12, 12, 11, 9, 6, 8, 11, 10, 10, 19, 6, 18, 11, 10, 12, 10, 10, 13, 10, 8, 11, 7, 10, 9, 17, 13, 14, 15, 11, 11, 11, 8, 12, 13, 9, 8, 9, 9, 8, 9, 16, 5, 7, 9, 10, 8, 12, 19, 9, 8, 19, 8, 4, 19, 6, 9, 11, 16, 6, 10, 2462298, 9, 8, 19, 9, 10, 11, 5, 11, 4, 3, 9, 16, 7, 11, 14, 12, 6, 7, 8, 10, 9, 9, 9, 20, 6, 21, 14, 9, 9, 9, 8, 7, 8, 18, 5, 12, 12, 12, 19, 8, 11, 11, 11, 17, 8, 9, 10, 12, 10, 3, 10, 10}

Returns: {-1 }
{9, 5, 11, 13, 9, 9, 11, 8, 10, 7, 15, 11, 8, 11, 12, 12, 9, 10, 9, 11, 11, 10, 12, 9, 10, 8, 6, 11, 11, 10, 8, 11, 16, 10, 6, 10, 13, 11, 8, 9, 11, 5, 11, 10, 7, 12, 10, 10, 12, 9, 12, 11, 9, 8, 10, 11, 10, 7, 5, 16, 8, 11, 8, 6, 7, 6, 16, 10, 10, 9, 16, 10, 11, 10, 8, 10, 10, 11, 11, 7, 12, 8, 14, 8, 7, 9, 11, 12, 10, 10, 7, 8, 3, 10, 13, 10, 7, 6, 9, 9, 12, 5, 10, 11, 9, 11, 13, 10, 8, 11, 14, 11, 4, 9, 7, 10, 9, 10, 8, 6, 9, 8, 5, 6, 13, 10, 9, 7, 9, 8, 12957690, 10, 7, 11, 5, 12, 8, 4, 10, 10, 10, 7, 5, 5, 10, 6, 5, 6, 10, 8, 9, 6, 11, 11, 8, 9, 6, 5, 10, 9, 7, 7, 11, 12, 5, 13, 9, 5, 13, 5, 14, 9, 8, 5, 10, 11, 6, 7, 6, 10, 12, 8, 10, 12, 10, 9, 11, 11, 12, 8, 4, 4, 15, 5, 8, 11, 6, 8, 9, 9, 11, 5, 4, 11, 10, 4, 7, 7, 7, 8, 14, 9, 25811816, 7, 7, 10, 12, 15, 12, 6, 8, 6, 9, 11, 10, 11, 7, 7, 7, 3, 11, 8, 9, 13, 8, 7, 6, 5, 4, 5, 12, 9, 12, 12, 9, 11, 8, 7, 10, 12, 8, 8, 10, 11, 10, 8, 7, 11, 7, 7, 7, 16, 11, 12, 10, 9, 8, 11, 2376912, 8, 9, 12, 9, 6, 10, 9, 6, 10, 7, 8, 10, 9, 12, 13, 9, 11, 10, 5, 11, 12, 9, 6, 6, 10, 8, 15, 9, 5, 12, 9, 10, 8, 12, 9, 15, 12, 9, 6, 15, 11, 9, 10, 9, 15, 7, 12, 14, 14, 7, 13, 7, 7, 6, 8, 6, 11, 7, 9, 9, 10, 5, 12, 4831, 13, 8, 10, 7, 12, 14, 9, 9, 16, 5, 6, 7, 11, 6, 10307022, 9, 9, 11, 7, 6, 8, 5, 15, 10, 9, 6, 8, 10, 8, 10, 14, 11, 6, 12, 7, 7, 8, 4, 4, 14, 14, 10, 11, 14, 7, 7, 9, 11, 9, 2, 8, 9, 15, 5, 10, 9, 6, 14, 7, 5, 8, 10, 8, 9, 10, 8, 7, 16, 15, 6, 14, 12, 6, 5, 16, 6, 6, 16, 15, 7, 9, 10, 12, 7, 9, 7, 12, 13, 8, 6, 14, 5, 13, 13, 8, 7, 8, 12, 13, 6, 10, 5, 10, 7, 7, 13, 10, 5, 15, 4, 7, 7, 11, 11, 10, 8, 10, 8, 12, 10, 11, 11, 7, 7, 6, 5, 6, 5, 11, 5, 8, 7, 8, 13, 11, 6, 8, 5, 11, 10, 8, 7, 9, 6, 8, 10, 11, 5, 14, 16, 8, 12, 7, 9, 7, 10, 8, 6, 15, 12, 13, 16, 8, 7, 7, 9, 11, 15, 10, 7, 8, 11, 8, 10, 10, 7, 6, 6, 11, 8, 10, 14, 15, 8, 6, 7, 8, 9, 6, 10, 12, 10, 4, 11, 5, 6, 8, 12, 15, 6, 6, 8, 4, 9, 13, 12, 16, 8, 7, 8, 3, 7, 14, 9, 8, 7, 6, 11, 9, 7, 6, 9, 5, 8, 9, 8, 8, 6, 4, 12, 5, 7, 12, 8, 9, 11, 6, 8, 10, 8, 8, 7, 8, 11, 10, 8, 5, 12, 6, 9, 10, 9, 9, 7, 13, 7, 7, 10, 7, 7, 13, 9, 9, 12, 8, 8, 8, 6, 13, 13, 6, 12, 11, 10, 15, 10, 5, 7, 12, 9, 9, 6, 10, 10, 7, 6, 10, 6, 10, 8, 7, 8, 9, 9, 9, 11, 16, 7, 13, 4, 8, 7, 13, 6, 12, 5, 12, 10, 7, 6, 7, 10, 5, 6, 6, 9, 6, 8, 9, 7, 12, 8, 7, 12, 10, 8, 7, 7, 6, 10, 9, 8, 10, 5, 4, 11, 8, 15, 12, 7, 8, 12, 8, 4, 15, 11, 10, 6, 7, 10, 11, 11, 7, 12, 14, 9, 13, 7, 12, 9, 10, 11, 5, 10, 9, 8, 9, 6, 6, 8, 15, 8, 7, 3, 13, 7, 7, 5, 10, 6, 14, 9, 8, 5, 10, 5, 5, 8, 10, 11, 14, 8, 8, 12, 9, 6, 6, 9, 11, 9, 8, 15, 12, 7, 10, 8, 6, 12, 11, 14, 11, 10, 7, 10, 10, 6, 6, 9, 11, 13, 10, 10, 6, 7, 11, 12, 10, 10, 11, 10, 12, 6, 6, 8, 8, 12, 4, 15, 7, 14, 14, 7, 5, 6, 8, 7, 8, 7, 11, 7, 10, 8, 6, 15, 11, 12, 7, 12, 10, 11, 10, 12, 8, 14, 12, 9, 7, 6, 10, 14, 6, 10, 14, 5, 5, 8, 8, 9, 9, 5, 10, 11, 13, 12, 11, 10, 9, 9, 8, 7, 11, 6, 7, 4, 9, 12, 7, 6, 7, 9, 6, 11, 12, 11, 11, 9, 9, 7, 5, 12, 15, 6, 11, 11, 6, 5, 7, 5, 10, 5, 9, 15, 12, 4, 12, 9, 1231386, 12, 13, 8, 13, 8, 9, 12, 9, 8, 12, 11, 6, 12, 8, 7, 12, 13, 5, 16, 10, 6, 10, 11, 10, 11, 8, 7, 10, 11, 9, 15, 8, 9, 11, 10, 7, 8, 8, 11, 6, 6, 7, 8, 9, 8, 8, 9, 8, 10, 10, 13, 12, 7, 6, 10, 8, 11, 12, 11, 7, 3, 8, 11, 7, 8, 10, 7, 7, 8, 10, 9, 9, 5, 13, 9, 9, 7, 7, 7, 12, 6, 7, 9, 11, 6, 7, 9, 8, 6, 12, 15, 16, 15, 7, 14, 10, 9, 7, 11, 9, 6, 10, 7, 11, 8, 10, 11, 8, 10, 4, 7, 6, 13, 12, 8, 7, 11, 11, 6, 9, 10, 8, 10, 8, 12, 7, 10, 8, 7, 6, 10, 14, 12}

Returns: {-1 }
{9, 10, 8, 8, 8, 11, 8, 8, 15, 12, 10, 5, 14, 12, 9, 11, 11, 7, 7, 9, 11, 11, 10, 8, 11, 9, 10, 12, 14, 10, 10, 9, 8, 12, 10, 5, 12, 7, 9, 13, 6, 9, 8, 8, 8, 9, 8, 10, 6, 3, 9, 9, 11, 12, 10, 14, 10, 5, 12, 3, 11, 6, 12, 11, 6, 13, 8, 10, 9, 9, 9, 7, 8, 11, 10, 5, 8, 7, 5, 9, 9, 6, 13, 10, 11, 12, 9, 11, 7, 9, 6, 9, 10, 5, 14, 7, 7, 7, 8, 9, 12, 10, 6, 13, 8, 8, 9, 12, 11, 7, 8, 6, 6, 7, 5, 8, 10, 9, 6, 5, 8, 8, 13406567, 8, 5, 9, 11, 7, 5, 11, 6, 7, 9, 13, 6, 12, 12, 14, 9, 5, 9, 9, 10, 8, 8, 15, 11, 12, 7, 140033, 8, 7, 5, 25303, 10, 5, 9, 5, 9, 9, 6, 7, 13, 11, 11, 6, 9, 9, 9, 10, 11, 8, 6, 7, 19308501, 6, 9, 9, 7, 8, 26086422, 10, 9, 6, 10, 12, 11, 7, 9, 9, 9, 10, 9, 14, 11, 9, 5, 7, 6, 4, 12, 8, 12, 7, 6, 8, 11, 9, 8, 10, 5, 8, 9, 11, 9, 6, 12, 6, 6, 8, 11, 5, 7, 12, 8, 9, 9, 10, 9, 11, 8, 8, 7, 9, 8, 6, 4, 7, 9, 10, 10, 11, 9, 11, 9, 10, 5, 8, 7, 8, 9, 8, 11, 11, 10, 10, 9, 9, 8, 7, 6, 8, 5, 4, 6, 13, 14, 9, 8, 6, 9, 8, 11, 13, 13, 13, 7, 13, 13, 12, 9, 9, 9, 8, 8, 10, 7, 6, 11, 6, 13, 9, 6, 11, 4, 9, 11, 13, 5, 11, 6, 7, 4, 6, 8, 8, 5, 8, 7, 13, 7, 7, 5, 5, 9, 8, 12, 10, 12, 5, 10, 14, 9, 13, 7, 2027, 10, 7, 1823, 7, 6, 9, 11, 11, 9, 11, 8, 9, 8, 6, 8, 11, 10, 13, 10, 9, 6, 7, 8, 10, 12, 3, 6, 8, 12, 10, 8, 6, 10, 14, 12, 1541, 10, 7, 5, 7, 9, 5, 10, 7, 11, 8, 9, 9, 11, 10, 8, 13, 9, 11, 2409, 9, 8, 21257878, 9, 9, 10, 9, 7, 4, 13, 8, 12, 6, 12, 10, 9, 6, 7, 10, 9, 7, 7, 6, 7, 6, 9, 8, 6, 10, 11, 9, 10, 10, 8, 7, 10, 10, 6, 10, 11, 8, 8, 5, 8, 8, 7, 13, 7, 6, 10, 6, 10, 8, 10, 8, 3, 8, 11, 8, 7, 8, 6, 8, 7, 10, 7, 8, 10, 8, 14, 4, 4, 9, 4, 10, 12, 7, 5, 4, 5, 9, 12, 10, 10, 6, 5, 11, 14, 9, 6, 10, 10, 10, 13, 5, 8, 11, 5, 9, 11, 11, 9, 8, 8, 7, 4, 7, 9, 6, 9, 8, 7, 6, 11, 9, 7, 5, 7, 734311, 104120, 9, 7, 11, 13, 11, 9, 7, 5, 6, 9, 14, 12, 7, 8, 5, 10, 12, 11, 10, 8, 10, 6, 8, 11, 10, 8, 9, 8, 10, 11, 11, 239686, 10, 8, 6, 8, 10, 8, 7, 4, 12, 6, 4, 13, 9, 13, 11, 3, 9, 11, 7, 10, 11, 9, 9, 8, 11, 9, 14, 8, 11, 12, 5, 8, 11, 11, 9, 11, 8, 7, 9, 8, 8, 8, 3, 8, 11, 9, 13, 7, 4, 11, 9, 12, 6, 6, 14, 9, 10, 9, 8, 6, 6, 6, 8, 6, 11, 8, 9, 12, 11, 7, 6, 8, 5, 9, 9, 9, 6, 13, 7, 10, 876325, 14, 9, 8, 16123623, 8, 8, 10, 9, 10, 9, 5, 6, 14, 4, 9, 9, 11, 7, 9, 11, 9, 7, 11, 10, 5, 11, 464986141, 6, 10, 12, 348717311, 10, 9, 12, 11, 6, 61916, 7, 5, 10, 8, 8, 9, 6, 9, 9, 9, 10, 9, 9, 11, 9, 10, 7, 11, 10, 11, 6, 8, 6, 10, 13, 17201606, 10, 8, 11, 5, 3, 10, 8, 12, 12, 11, 9, 8, 8, 6, 12, 7, 11, 8, 13, 8, 9, 8, 8, 13, 11, 8, 10, 7, 8, 10, 9, 9, 8, 10, 8, 10, 9, 9, 5, 10, 4, 6, 11, 8, 10, 13, 7, 11, 10, 9, 5, 12, 9, 7, 10, 327853, 8, 12, 10, 9, 9, 6, 5, 9, 6, 10, 12, 8, 8, 9, 11, 6, 4, 12, 6, 5, 13, 7, 11, 6, 10, 5, 11, 11, 7, 8, 12, 10, 7, 7, 5, 8, 9, 8, 12, 9, 20640702, 10, 11, 6, 5, 11, 11, 8, 9, 10, 8, 5, 8, 9, 7, 13, 9, 9, 9, 10, 11, 7, 9, 9, 13, 10, 11, 7, 11, 8, 6, 10, 12, 7, 10, 4, 7, 11, 6, 8, 11, 10, 13, 8, 6, 9, 9, 11, 8, 3, 10, 12, 13, 13, 9, 9, 7, 13, 11, 8, 8, 8, 9, 7, 6, 11, 5, 8, 14, 6, 12, 10, 6, 4, 7, 7, 12, 9, 10, 11, 8, 8, 8, 13, 9, 10, 8, 9, 10, 6, 9, 9, 12, 10, 9, 5, 8, 7, 9, 12, 11, 9, 8, 10, 9, 12, 11, 10, 7, 12, 9, 14, 41635278, 10, 8, 7, 8, 11, 10, 9, 8, 8, 12, 10, 11, 8, 7, 10, 9, 13, 11, 6, 10, 9, 8, 10, 14, 11, 8, 10, 11, 12, 6, 8, 6, 11, 5, 5, 8, 6, 9, 8, 8, 8, 13, 8, 9, 10, 7, 8, 8, 7, 10, 9, 10, 6, 5, 4, 11, 6, 8, 15, 12, 7, 9, 11, 10, 9, 10, 11, 8, 4, 8, 6, 8, 12, 9, 5, 7, 8, 10, 9, 13, 10, 11, 7, 11, 8, 11, 6, 7, 8, 5, 11, 14, 9, 11, 301745549, 6, 7, 10, 5, 16973954, 11, 12, 8, 9, 5, 8, 8, 11, 11, 9, 9}

Returns: {-1 }
{7, 11, 13, 10, 10, 13, 9, 11, 14, 10, 10, 10, 10, 8, 5, 12, 15, 6, 9, 10, 4, 5, 12, 10, 12, 8, 9, 6, 7, 14, 11, 10, 7, 9, 8, 12, 8, 8, 7, 6, 5, 7, 6, 10, 13, 15, 7, 14, 10, 15, 5, 2, 8, 9, 14, 13, 9, 11, 12, 7, 15, 14, 15, 8, 8, 8, 5, 8, 11, 12, 12, 16, 7, 5, 129411981, 8, 8, 12, 7, 10, 8, 13, 7, 11, 5, 13, 7, 7, 10, 12, 6, 11, 7, 9, 16, 8, 12, 10, 11, 6, 12, 10, 14, 10, 7, 9, 20715, 15, 12, 6, 8, 12, 16, 6, 11, 8, 10, 10, 5, 6, 9, 4, 10, 12, 8, 7, 15, 10, 10, 13, 10, 13, 10, 6, 10, 679731, 6, 6, 10, 5, 7, 6, 13, 10, 9, 10, 11, 16, 7, 4, 11, 15, 12, 10, 11, 12, 13, 5, 6, 8, 12, 7, 11, 13, 10, 13, 12, 6, 11, 15, 7, 8, 12, 11, 6, 8, 12, 10, 15, 11, 14, 12, 11, 11, 6, 6, 12, 8, 9, 8, 14, 8, 16, 6, 9, 7, 9, 11, 9, 15, 48843, 12, 12, 6, 8, 7, 6, 10, 13, 6, 7, 5, 8, 14, 6, 17, 14, 10, 13, 10, 9, 7, 13, 11, 14, 11, 7, 13, 8, 10, 14, 7, 16, 11, 11, 7, 7, 8, 8, 7, 7, 9, 11, 10, 13, 11, 12, 11, 8, 11, 8, 10, 7, 14, 13, 6, 15, 14, 9, 12, 11, 11, 16, 6, 11, 8, 9, 9, 13, 5, 11, 5, 9, 6, 5, 11, 5, 8, 11, 9, 8, 12, 10, 6, 9, 15, 13, 10, 2, 9, 8, 12, 11, 6, 13, 8, 15, 11, 14, 7, 4, 11, 9, 9, 6, 6, 8, 12, 10, 12, 11, 6, 11, 9, 10, 8, 6, 8, 16, 7, 8, 8, 6, 10, 9, 14, 8, 9, 10, 9, 11, 13, 9, 10, 7, 8, 8, 14000701, 9, 10, 11, 7, 13, 8, 13, 5, 7, 5, 10, 4, 6, 9, 9, 14, 10, 13, 13, 6, 6, 11, 12, 11, 7, 14, 12, 7, 6, 11, 9, 6, 11, 9, 12, 11, 12, 5, 9, 8, 6, 7, 15, 7, 12, 5, 6, 16, 6, 8, 10, 7, 7, 6, 12, 9, 9, 8, 6, 9, 9, 12, 8, 11, 14, 11, 6, 13, 11, 11, 9, 8, 14, 8, 9, 12, 9, 16, 10, 12, 11, 13, 6, 6, 15, 14, 5, 11, 11, 9, 5, 11, 13, 9, 12, 7, 8, 10, 9, 10, 10, 11, 15, 17, 11, 12, 6, 14, 8, 5, 5, 6, 11, 16, 17163, 10, 9, 16, 10, 7, 9, 11, 4, 17, 11, 9, 14, 11, 9, 6, 6, 11, 10, 6, 7, 13, 8, 7, 14, 12, 14, 9, 15, 6, 9, 8, 13, 5, 11, 12, 7, 14, 10, 10, 7, 11, 6, 6, 9, 7, 8, 11, 5, 6, 5, 9, 12, 13, 12, 13, 9, 16, 42433, 11, 6, 13, 10, 11, 11, 6, 15, 9, 6, 11, 17, 6, 8, 15, 4, 14, 12, 9, 8, 10, 8, 13, 12, 12, 12, 10, 9, 7, 10, 11, 9, 7, 7, 5, 10, 7, 6, 8, 9, 9, 8, 13, 7, 10, 8, 12, 9, 16, 6, 13, 8, 6, 9, 12, 6, 8, 6, 16, 13, 11, 7, 12, 6, 10, 11, 6, 12, 13, 13, 6, 6, 14, 11, 11, 8, 8, 14, 7, 10, 5, 9, 9, 9, 5, 8, 11, 7, 5, 13, 9, 11, 10, 14, 11, 8, 5, 16, 17, 14, 14, 14, 9, 6, 9, 10, 4, 6, 8, 515564998, 10, 10, 11, 12, 7, 13, 4, 8, 8, 15, 7, 8, 5, 13, 10, 12, 11, 8, 7, 6, 9, 9, 11, 8, 14, 10, 8, 16, 6, 8, 13, 14, 14, 11, 11, 7, 8, 12, 8, 15, 13, 8, 13, 9, 8, 13, 3, 7, 10, 11, 7, 15, 16, 11, 5, 8, 8, 8, 10, 10, 11, 12, 9, 7, 12, 12, 8, 5, 11, 5, 6, 11, 10, 14, 15, 14, 13, 8, 8, 11, 11, 8, 12, 7, 9, 9, 12, 9, 4, 12, 15, 6, 9, 14, 10, 4, 9, 12, 9, 10, 13, 14, 9, 13, 16, 7, 13, 9, 10, 6, 9, 10, 11, 8, 8, 8, 8, 10, 10, 14, 12, 14, 6, 10, 10, 13, 12, 6, 13, 4, 3, 14, 7, 7, 9, 8, 6, 15, 10, 10, 8, 11, 14, 8, 9, 9, 9, 6, 11, 5, 11, 7, 11, 9, 7, 11, 5, 8, 10, 14, 7, 11, 9, 10, 7, 7, 11, 9, 10, 10, 5, 7, 7, 8, 14, 12, 6, 7, 6, 8, 13, 10, 9, 10, 14, 9, 14, 8, 9, 10, 10, 8, 16, 8, 11, 13, 10, 4, 12, 9, 7, 16, 8, 7, 8, 12, 10, 9, 13, 11, 11, 6, 13, 8, 12, 7, 15, 9, 13, 8, 9, 14, 12, 11, 15, 11, 8, 13, 9, 11, 10, 6, 16, 11, 8, 13, 9, 14, 8, 7, 16, 8, 8, 11, 10, 12, 15, 10, 11, 11, 16, 10, 9, 16, 15, 7, 10, 7, 12, 5, 11, 8, 8, 7, 11, 6, 10, 10, 10, 6, 6, 13, 8, 14, 5, 5, 8, 7, 15, 8, 7, 6, 14, 10, 7, 7, 11, 13, 8, 4, 8, 9, 7, 5, 4, 14, 14, 9, 8, 12, 10, 14, 12, 7, 9408, 6, 7, 11, 14, 11, 11, 9, 7, 9, 8, 7, 11, 6, 7, 6, 8, 4, 15, 7, 6, 6, 12, 2, 7, 11, 11, 5, 13, 10, 6, 6, 5, 8, 6, 15, 7, 9, 9, 17, 14, 9, 6, 12, 5, 10, 13, 11, 9, 10, 8, 7, 7, 6, 8, 12, 14, 11, 13, 11, 7, 5, 8, 13, 10, 8, 7, 12, 8, 8, 8}

Returns: {-1 }
{9, 10, 7, 13, 8, 13, 7, 6, 13, 5, 11, 7, 9, 11, 8, 14, 9, 13, 5, 15, 8, 6, 7, 9, 5, 6, 9, 13, 9, 10, 10, 14, 4, 13, 7, 32026264, 15, 6, 6, 5, 12, 9, 10, 13, 6, 12, 11, 6, 9, 11, 5, 8, 10, 14, 12, 9, 2664, 11, 7, 10, 3, 8, 9, 9, 10, 10, 8, 10, 8, 13, 11, 8, 8, 338152, 11, 62909, 7, 7, 8, 7, 11, 9, 3, 8, 9, 10, 5, 7, 12, 11, 9, 8, 8, 11, 7, 8, 20540024, 11, 6, 15, 7142, 7, 10, 9, 4, 7, 5, 7, 9, 10, 14, 10, 10, 7627, 9, 7, 12, 7, 12, 7, 9, 12, 11, 9, 10, 9, 11, 10, 9, 11, 2088, 9, 9, 8, 13, 5, 7, 8, 10051500, 10, 7, 8, 7, 9, 10, 9, 11, 9, 8, 6, 9, 9, 12, 11, 9, 8, 10, 10, 7, 13, 5, 11, 9, 13, 9, 13, 6, 10, 6, 8, 6, 4, 8, 13, 12, 12, 10, 13, 21449, 6, 13, 12, 5, 5, 6, 8, 6, 13, 11, 9, 7, 9, 8, 9, 11, 10, 7, 506350, 11, 5, 9, 12, 13, 10, 5, 6, 7, 7, 6, 5, 11, 8, 3, 9, 96059, 151537, 8, 7, 10, 11, 6, 13, 8, 13, 9, 7, 13, 4, 6, 11, 10, 6, 6, 7, 13, 10, 13, 10, 10, 7, 11, 8, 8, 8, 103828981, 4, 5, 10277703, 7, 6, 9, 3, 13, 11, 11, 8, 13, 11, 7, 164739438, 5, 9, 6, 7, 11, 6, 9, 6, 13, 12, 12, 9, 13, 9, 5, 11, 5, 6, 10, 6, 8, 8, 12, 9, 7, 8, 4, 12, 9, 8, 25159, 8, 11, 12, 5, 7, 9, 6830, 6, 6, 5, 6, 10, 12, 11, 13, 9, 5, 11, 7, 11807988, 13, 9, 5, 9, 12, 9, 7, 42752, 9, 8, 8, 12, 13, 9, 5, 8, 11, 11, 9, 7, 11, 8, 9, 4, 9, 8, 9, 8, 16635080, 6, 7, 6, 15, 11, 6, 285202950, 5, 13, 5, 6, 5, 12, 5, 5, 4, 2880707, 11, 6, 11, 5, 11, 9, 5, 7, 8, 7, 5, 9, 16, 8, 11, 11, 8, 8, 11, 8, 16, 12, 8, 9, 7, 11, 7, 8, 6, 7, 11, 5, 7, 10, 5, 10, 11, 6, 11, 10, 6, 5, 8, 10, 6, 13, 12, 8, 10, 7, 11, 9, 12, 13, 7, 13, 10, 11, 7, 8, 6, 5, 9, 10, 13, 8, 11, 9, 13, 8, 13, 13, 11, 8, 5, 11, 9, 13, 10, 6, 8, 7, 9, 25050, 2617441, 7, 7, 9, 10, 135894997, 11, 6, 10, 8, 6, 11, 11, 8, 10, 11, 8, 6, 10, 9, 12, 9, 10, 5, 7, 11, 6, 9, 6, 9, 4, 7, 11, 9, 9, 5, 38194819, 8, 10, 8, 5, 6, 12, 11, 10, 9, 14, 214923, 12, 11, 9, 13, 13, 11, 7, 9, 9, 7863, 7, 10, 9, 10, 5, 7, 7, 6, 4, 9, 7, 7, 6, 7, 5, 11, 9, 10, 8, 1568, 14, 13, 9, 10, 6, 10, 13, 9, 9, 7, 9, 11, 7, 11, 6, 12, 8, 14, 11, 12, 6, 13, 8, 8, 8, 12, 13, 8, 17, 9, 11, 8, 9, 13, 7, 10, 9, 11, 4, 6, 343864824, 5, 8, 6, 9, 10, 9, 8, 6, 9, 12, 10, 6, 10, 9, 9, 8, 11, 8, 7, 9, 6, 5, 10, 11, 12, 6, 13, 11, 12, 9, 6, 9, 16, 10, 740535, 10, 7, 12, 4, 11, 12, 13, 1565100, 14, 5, 8, 6, 11, 11, 11, 8, 13, 7, 6, 8, 10, 5, 9, 15, 6, 6, 13, 6, 5, 7, 12, 8, 10, 11, 9, 6, 8, 8, 10, 9, 6, 8, 8, 8, 12, 7, 14, 6, 11, 9, 9, 6, 8, 6, 13, 8, 8, 6, 13, 9, 9, 3426042, 9, 318620, 9, 6, 8, 7, 10, 8, 9, 9, 6, 13, 8, 7, 13, 6, 12, 7, 394969435, 10, 10, 7, 9, 10, 6, 9, 9, 5, 6, 8, 6, 10, 6, 6, 5, 13, 6, 11, 13, 3, 8, 13, 11, 9, 17, 11, 6, 10, 6, 9, 10, 8, 8, 3, 9, 8, 6, 12, 8, 9, 8, 9, 7, 10, 6, 5, 8, 4, 8, 9, 15, 8, 9, 6, 9, 11, 14, 4, 4, 7, 5, 6, 11, 11, 7, 11, 11, 8, 112405912, 13, 853366, 13, 13, 13, 4, 8, 13, 9, 9, 21346704, 10, 14, 7, 7, 6, 5, 11, 9, 11, 10, 16, 9, 9, 8, 4, 13, 12, 4, 7, 9, 8, 13, 12, 9, 21332, 10, 9, 5, 163725, 8, 7, 4, 13, 8, 5, 8, 6, 8, 13, 13, 5, 8, 5, 7, 9, 11, 6, 9, 4, 12, 9533, 5, 7, 8, 8, 6, 11, 7, 10, 9, 2735126, 9, 10, 14, 12, 10, 7, 9, 6, 5, 11, 6, 11, 8, 10, 12, 15, 3, 14, 9, 29923, 11, 9, 8, 9, 11, 7, 17, 7, 7, 5, 11, 6, 5, 8, 7, 7, 8, 8, 10, 59858, 6, 9, 8, 7, 9, 11, 7, 14, 8, 9, 11, 13, 6, 8, 4, 12, 12, 12, 12, 5, 11, 9, 13, 11, 10, 11, 11, 8, 7, 10, 10, 10, 8, 12, 13, 9, 9, 12, 13, 8, 16, 10, 8, 12, 13, 6, 6, 11, 6, 10, 9, 7, 6, 13, 12, 8, 11, 7, 11, 11, 8, 12, 7, 11, 8, 8, 11, 7, 10, 9, 10, 11, 5, 8, 12, 8, 8, 394213336, 11, 8, 11, 7, 9, 8, 9, 10, 7, 10, 11, 7, 9, 11, 9, 8, 9, 10, 12, 5, 10, 10, 8, 6, 14, 5, 10, 5, 9, 7, 13, 11, 10, 10, 9, 13, 12, 6, 10, 5, 9, 12, 27359, 728154, 6722498, 12, 7, 13, 12, 7, 10, 11, 9, 8, 11, 8, 6585348, 12, 7, 7, 10, 10, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{15, 7, 6, 6, 9, 8, 11, 5, 5, 7, 10, 7, 17, 7, 11, 7, 12, 7, 5, 11, 6, 11, 11, 11, 11, 9, 7, 8, 9, 11, 8, 13, 7, 11, 12, 6, 17, 8, 8, 9, 12, 10, 10, 15, 9, 11, 9, 7, 8, 6, 12, 10, 9, 8, 16, 7, 9, 12, 8, 7, 7, 10, 10, 8, 5, 10, 11, 7, 9, 8, 10, 9, 7, 9, 9, 7, 6, 9, 7, 10, 9, 9, 11, 16, 12, 7, 8, 11, 6, 8, 8, 9, 7, 9, 10, 9, 6, 10, 6, 4, 11, 6, 12, 8, 10, 6, 8, 7, 9, 6, 9, 6, 9, 8, 6, 8, 11, 9, 7, 8, 10, 17, 9, 7, 10, 7, 9, 8, 13, 13, 6, 9, 10, 4, 12, 8, 13, 14, 7, 6, 7, 12, 6, 8, 13, 12, 6, 7, 10, 16, 6, 7, 7, 16, 6, 12, 13, 9, 14, 10, 11, 9, 7, 11, 8, 11, 7, 8, 13, 7, 14, 6, 8, 8, 9, 10, 14, 8, 7, 5, 9, 14, 11, 13, 12, 6, 9, 8, 9, 7, 8, 9, 7, 9, 377667, 9, 10, 10, 6, 9, 10, 11, 9, 5, 9, 7, 10, 5, 10, 9, 10, 9, 8, 11, 8, 8, 6, 10, 9, 8, 9, 9, 10, 11, 7, 9, 3, 14, 9, 7, 6, 4, 5, 7, 10, 11, 5, 13, 7, 8, 6, 7, 6, 10, 10, 14, 8, 14, 8, 7, 9, 10, 8, 10, 7, 6, 7, 8, 9, 7, 7, 8, 8, 16, 4, 6, 6, 7, 11, 4, 6, 8, 5, 9, 5, 13, 8, 10, 5, 12, 9, 10, 10, 9, 11, 6, 13, 5, 7, 7, 14, 8, 15, 11, 7, 10, 4, 3, 6, 11, 9, 9, 8, 8, 7, 7, 6, 8, 9, 14, 9, 9, 12, 8, 8, 6, 12, 8, 186195782, 9, 9, 7, 8, 13, 8, 12, 6, 14, 10, 11, 8, 7, 11, 8, 5, 10, 16, 6, 14, 7, 7, 10, 6, 7, 9, 5, 9, 10, 6, 10, 9, 6, 6, 8, 7, 7, 5, 10, 12, 14, 3, 9, 7, 6, 10, 9, 15, 13, 16, 11, 10, 13, 8, 11, 13, 7, 10, 4, 8, 7, 6, 9, 9, 6, 13, 15, 9, 8, 9, 9, 11, 9, 7, 9, 8, 10, 6, 8, 14, 14, 8, 8, 13, 10, 7, 8, 13, 8, 8, 7, 11, 10, 16, 9, 8, 12, 8, 9, 7, 9, 7, 8, 6, 11, 11, 6, 10, 7, 9, 7, 6, 14, 10, 12, 7, 10, 11, 15, 9, 8, 11, 6, 10, 6, 8, 10, 8, 7, 8, 12, 8, 7, 10, 6, 10, 15, 6, 9, 9, 8, 6, 9, 5, 8, 7, 10, 10, 5, 9, 11, 4, 5, 10, 9, 8, 10, 7, 9, 5, 10, 10, 9, 6, 17, 9, 11, 9, 5, 9, 8, 8, 9, 8, 10, 4, 8, 13, 7, 8, 12, 8, 12, 5, 13, 11, 8, 10, 6, 5, 10, 14, 9, 8, 6, 9, 10, 5, 12, 7, 8, 7, 10, 5, 12, 8, 14, 12, 6, 5, 10, 10, 4, 8, 14, 6, 6, 9, 9, 9, 16, 7, 10, 8, 9, 5, 9, 9, 11, 10, 13, 5, 8, 11, 11, 11, 8, 8, 8, 14, 15, 5, 8, 14, 10, 14, 11, 6, 10, 11, 7, 9, 9, 8, 14, 9, 8, 7, 10, 7, 8, 8, 6, 9, 9, 9, 13, 9, 6, 11, 9, 7, 7, 8, 6, 6, 11, 8, 11, 9, 5, 12, 9, 6, 10, 9, 8, 7, 10, 12, 10, 11, 10, 7, 8, 7, 10, 14, 8, 9, 10, 9, 3, 11, 9, 13, 13, 10, 7, 3, 8, 6, 8, 6, 12, 4, 7, 7, 8, 9, 9, 9, 5, 11, 8, 10, 9, 13, 8, 14, 11, 8, 8, 7, 14, 14, 8, 9, 5, 8, 3, 13, 8, 10, 5, 11, 8, 10, 7, 4, 3, 13, 11, 10, 8, 9, 5, 6, 11, 7, 8, 8, 11, 8, 9, 9, 16, 7, 7, 6, 9, 9, 7, 11, 8, 17, 9, 10, 9, 9, 7, 4, 10, 10, 5, 11, 7, 4, 7, 7, 10, 10, 7, 17, 11, 10, 13, 10, 10, 7, 7, 9, 8, 11, 9, 8, 11, 15, 7, 14, 11, 9, 6, 7, 9, 7, 6, 6, 10, 10, 10, 13, 6, 10, 8, 7, 14, 4, 11, 10, 5, 6, 6, 8, 10, 11, 5, 6, 9, 10, 8, 9, 12, 5, 7, 9, 8, 8, 8, 8, 5, 6, 10, 6, 4, 5, 7, 10, 7, 10, 8, 8, 9, 6, 6, 8, 12, 14, 9, 3, 12, 10, 6, 8, 8, 8, 9, 14, 7, 8, 9, 10, 11, 10, 11, 10, 9, 7, 16, 7, 5, 16, 10, 9, 11, 10, 6, 7, 9, 11, 6, 12, 7, 6, 8, 10, 8, 10, 8, 12, 6, 6, 7, 14, 11, 7, 12, 5, 6, 10, 6, 10, 10, 6, 9, 7, 9, 14, 6, 4, 9, 13, 10, 7, 9, 11, 8, 15, 9, 8, 9, 7, 12, 6, 7, 5, 10, 9, 5, 9, 13, 8, 7, 8, 11, 8, 9, 12, 10, 9, 10, 7, 11, 7, 6, 7, 4, 15, 9, 6, 8, 9, 6, 11, 5, 7, 8, 10, 9, 5, 9, 8, 14, 15, 11, 7, 13, 13, 7, 14, 12, 3, 9, 9, 9, 8, 8, 10, 7, 8, 9, 8, 8, 6, 8, 9, 8, 9, 11, 9, 6, 8, 8, 12, 9, 10, 9, 9, 5, 6, 6, 9, 13, 16, 6, 10, 12, 8, 7, 9, 7, 7, 11, 9, 10, 8, 8, 17592, 10, 7, 8, 10, 14, 8, 10, 7, 8, 15, 8, 5, 11, 8, 8, 6, 7, 11, 12, 8, 12, 6, 5, 6, 9, 8, 7, 9, 6, 10, 5, 10, 8, 9, 11, 7, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{7, 8, 9, 10, 7, 11, 6, 7, 10, 11, 6, 12, 8, 5, 8, 9, 6, 5, 5, 12, 5, 9, 8, 8, 10, 9, 5, 9, 7, 12, 10, 6, 8, 9, 8, 8, 10, 4, 7, 8, 4, 7, 11, 12, 13, 10, 9, 9, 12, 13, 10, 4, 6, 8, 4, 9, 9, 11, 9, 5, 8, 3, 7, 7, 6, 7, 12, 8, 11, 7, 9, 8, 3, 9, 10, 8, 8, 7644, 9, 8, 9, 9, 7, 7, 7, 6, 7, 8, 6, 5, 9, 9, 9, 10, 8, 6, 7, 9, 9, 16, 5, 8, 8, 9, 10, 10, 9, 8, 7, 8, 12, 7, 7, 9, 4, 8, 9, 10, 7, 12, 6, 8, 4, 7, 6, 11, 8, 8, 13, 7, 9, 8, 11, 6, 4, 15, 9, 8, 13, 9, 10, 5, 7, 10, 6, 8, 10, 9, 15, 8, 9, 9, 15, 13, 7, 12, 6, 8, 11, 7, 10, 6, 8, 15, 6, 9, 269632, 13, 9, 11, 7, 8, 8, 8, 13, 12, 13, 10, 99706, 8, 8, 9, 10, 7, 7, 5, 9, 8, 11, 5, 9, 12, 10, 10, 8, 9, 14, 7, 10, 11, 6, 8, 15, 10, 7, 8, 9, 3, 8, 11, 7, 5, 6, 10, 9, 7, 10, 7, 7, 11, 5, 9, 9, 10, 8, 6, 11, 9, 9, 14, 10, 8, 3, 5, 9, 7, 10, 7, 7, 5, 8, 9, 11, 13, 7, 10, 8, 13, 7, 7, 10, 12, 9, 12, 4, 7, 11, 9, 4, 9, 7, 10, 14, 9, 12, 10, 9, 7, 10, 11, 10, 9, 8, 8, 12, 8, 12, 5, 10, 13, 8, 10, 10, 8, 9, 10, 13, 5, 6, 7, 8, 9, 9, 16909256, 7, 8, 11, 7, 8, 7, 8, 7, 8, 8, 6, 4, 6, 6, 9, 8, 9, 9, 7, 9, 11, 12, 10, 10, 8, 6, 7, 12, 9, 11, 10, 6, 11, 11, 10, 12, 7, 8, 5, 7, 10, 11, 9, 10, 6, 10, 12, 12, 8, 10, 9, 7, 8, 9, 8, 10, 7, 8, 9, 6, 8, 6, 4, 9, 8, 4, 8, 8, 8, 8, 9, 7, 8, 8, 27622527, 11, 10, 7, 9, 10, 10, 8, 8, 7, 9, 13, 6, 15, 7, 6, 7, 8, 12, 7, 13, 7, 9, 9, 8, 8, 7, 11, 9, 7, 8, 13, 12, 8, 8, 9, 9, 4, 9, 9, 8, 8, 8, 10, 10, 9, 8, 6, 10, 7, 13, 9, 8, 8, 9, 11, 9, 8, 6, 8, 11, 8, 13, 8, 9, 8, 9, 11, 8, 10, 5, 5, 10, 9, 7, 10, 1212, 8, 7, 10, 9, 10, 8, 13, 9, 11, 8, 8, 6, 9, 9, 7, 8, 12, 10, 8, 7, 10, 8, 8, 8, 12, 8, 8, 12, 5, 6, 10, 8, 12, 9, 9, 8, 5, 8, 7, 7, 7, 5, 8, 10, 8, 6, 13, 6, 8, 11, 6, 7, 9, 3048, 8, 6, 5, 11, 7, 9, 10, 8, 10, 8, 7, 11, 10, 9, 6, 8, 10, 8, 11, 7, 15, 9, 10, 8, 11, 5, 9, 7, 15, 7, 10, 9, 11, 8, 13, 6, 9, 8, 9, 8, 12, 11, 8, 8, 5, 8, 10, 7, 4, 16, 7, 9, 6, 8, 15, 8, 10, 8, 12, 6, 9, 12, 6, 7, 7, 8, 10, 8, 7, 8, 11, 6, 11, 3, 9, 6, 11, 6, 6, 8, 8, 9, 9, 9, 8, 9, 10, 12, 9, 7, 7, 4, 9, 5, 10, 8, 9, 8, 6, 10, 7, 7, 10, 9, 10, 10, 7, 8, 8, 12, 6, 13, 9, 11, 7, 8, 12, 7, 10, 9, 6, 10, 10, 7, 8, 8, 2476900, 8, 13, 12, 7, 12, 7, 10, 7, 12, 10, 10, 7, 8, 4, 7, 12, 10, 9, 7, 5, 9, 7, 11, 9, 5, 7, 10, 14, 11, 5, 8, 6, 9, 11, 12, 15, 10, 9, 11, 9, 10, 4, 7, 10, 8, 11, 13, 7, 8, 6, 7, 12, 8, 10, 9, 10, 4, 15, 6, 8, 9, 10, 10, 11, 12, 8, 8, 7, 8, 10, 7, 10, 6, 7, 8, 7, 8, 9, 10, 7, 8, 9, 10, 8, 9, 9, 7, 16, 13, 10, 4, 9, 9, 8, 10, 8, 8, 14, 7, 7, 7, 7, 11, 7, 5, 7, 8, 8, 8, 9, 6, 9, 6, 12, 7, 9, 9, 10, 9, 9, 7, 9, 12, 9, 9, 4, 12, 4, 10, 8, 11, 7, 6, 12, 8, 9, 10, 5, 13, 11, 7, 12, 8, 9, 8, 10, 5, 11, 14, 8, 10, 8, 8, 6, 5, 7, 6, 11, 7, 8, 8, 11, 10, 5, 8, 14, 7, 11, 11, 5, 8, 5, 7, 8, 9, 12, 10, 9, 9, 6, 9, 10, 13, 10, 9, 13, 7, 7, 8, 9, 8, 7, 8, 6, 5, 7, 8, 6, 10, 8, 8, 4, 7, 10, 9, 9, 11, 9, 12, 8, 9, 10, 6, 10, 4, 9, 10, 13, 9, 4, 7, 9, 8, 7, 10, 13, 7, 8, 8, 6, 9, 7, 7, 10, 9, 7, 10, 9, 11, 7, 13, 10, 7, 7, 4, 12, 9, 13, 7, 7, 5, 13, 7, 7, 12, 6, 9, 9, 12, 12, 8, 8, 6, 7, 9, 12, 2, 12, 10, 14, 6, 12, 8, 11, 8, 8, 12, 6, 8, 7, 10, 9, 9, 9, 9, 11, 10, 11, 13, 9, 9, 10, 8, 5, 12, 6, 10, 8, 10, 11, 8, 5, 7, 6, 12, 9, 8, 6, 5, 7, 8, 11, 7, 7, 10, 8, 9, 9, 9, 8, 7, 9, 9, 6, 6, 10, 6, 7, 13, 8, 7, 12, 6, 7, 9, 7, 5, 271142, 11, 12, 10, 7, 6, 9, 13, 9, 7, 10, 9, 7, 8, 12, 11, 11, 6, 8, 9, 9, 12, 10, 12, 11, 7, 6}

Returns: {-1 }
{8, 5, 7, 9, 9, 12, 5, 11, 9, 4, 8, 8, 12, 12, 10, 8, 11, 9, 8, 10, 6, 8, 8, 9, 7, 9, 8, 10, 10, 11, 6, 11, 8, 9, 14, 14, 7, 9, 10, 875177, 19, 8, 12, 8, 8, 7, 17, 7, 10, 9, 7, 8, 9, 8, 12, 8, 15, 11, 9, 8, 3, 7, 12, 4, 14, 7, 11, 10, 13, 8, 11, 10, 7, 9, 6, 6, 6, 16, 7, 4, 7, 13, 13, 6, 7, 10, 8, 10, 7, 9, 7, 8, 10, 8, 9, 16, 9, 10, 8, 12, 13, 7, 8, 11, 9, 10, 11, 11, 7, 6, 11, 10, 8, 4, 9, 12, 10, 12, 8, 11, 5, 10, 14, 10, 9, 5, 12, 15, 8, 11, 5, 9, 14, 15, 7, 10, 10, 6, 15, 7, 6, 9, 8, 8, 16, 8, 11, 11, 9, 9, 16, 6, 16, 13, 6, 8, 8, 10, 15, 12, 7, 7, 5, 7, 12, 8, 9, 10, 4, 6, 9, 10, 13, 14, 10, 13, 7, 8, 7, 7, 8, 9, 8, 10, 10, 7, 9, 8, 12, 10, 11, 8, 10, 13, 10, 7, 8, 12, 12, 6, 13, 11, 14, 8, 8, 8, 9, 6, 8, 7, 7, 7, 11, 10, 9, 10, 8, 5, 10, 8, 11, 7, 9, 8, 7, 4, 14, 6, 19, 9, 9, 5, 12, 12, 8, 12, 12, 10, 14, 9, 15, 4, 11, 7, 10, 16, 11, 8, 10, 11, 8, 18, 11, 9, 10, 7, 13, 12, 7, 6, 6, 19, 5, 14, 12, 10, 7, 9, 9, 9, 7, 10, 8, 12, 6, 9, 6, 14, 11, 9, 14, 7, 6, 8, 6, 8, 10, 9, 17, 10, 9, 8, 7, 8, 11, 6, 12, 13, 2, 10, 8, 10, 5, 7, 10, 8, 6, 10, 7, 13, 5, 15, 8, 17, 11, 17, 9, 9, 7, 10, 9, 8, 9, 13, 11, 19, 6, 5, 10, 12, 6, 5, 11, 19, 9, 8, 7, 8, 9, 8, 12, 7, 9, 9, 7, 7, 3, 9, 15, 9, 10, 18, 8, 10, 9, 7, 9, 16, 19, 6, 10, 12, 9, 18, 7, 11, 11, 8, 11, 15, 16, 10, 13, 4, 10, 9, 6, 10, 7, 10, 15, 7, 9, 11, 6, 15, 8, 8, 8, 10, 14, 9, 8, 5, 13, 11, 8, 9, 161783, 16, 16, 9, 17, 16, 13, 16, 6, 13, 8, 11, 12, 3, 10, 10, 10, 7, 9, 14, 8, 11, 8, 8, 7, 10, 8, 14, 6, 8, 8, 8, 9, 6, 9, 7, 7, 14, 6, 6, 6, 5, 10, 16, 8, 5, 10, 10, 7, 12, 7, 7, 9, 9, 17, 7, 11, 13, 15, 10, 9, 14, 12, 8, 12, 10, 9, 10, 12, 8, 11, 6, 6, 13, 5, 11, 6, 8, 7, 16, 9, 8, 13, 13, 16, 13, 7, 9, 10, 4, 11, 8, 12, 10, 7, 54795324, 7, 11, 4, 8, 6, 5, 6, 10, 7, 8, 10, 8, 12, 9, 7, 8, 401376, 8, 8, 10, 11, 15, 9, 9, 7, 19, 4, 12, 9, 8, 9, 8, 4, 8, 10, 10, 10, 7, 6, 10, 9, 5, 8, 9, 11, 9, 13, 10, 7, 6, 10, 9, 8, 8, 4, 5, 10, 8, 9, 11, 9, 14, 7, 8, 15, 16, 10, 7, 8, 12, 7, 4, 8, 13, 12, 16, 14, 18, 16, 11, 12, 14, 10, 8, 9, 11, 11, 8, 6, 6, 9, 13, 10, 11, 8, 9, 5, 7, 6, 8, 10, 13, 6, 16, 9, 7, 8, 7, 9, 8, 14, 13, 7, 10, 16, 6, 8, 15, 5, 13, 12, 6, 4, 10, 9, 4, 6, 14, 10, 6, 8, 8, 4, 12, 7, 6, 6, 8, 9, 11, 8, 13, 5, 4, 6, 9, 8, 16, 15, 7, 6, 10, 9, 12, 17, 8, 8, 7, 5, 6, 9, 7, 9, 6, 8, 8, 5, 5, 8, 9, 7, 7, 7, 8, 9, 10, 18, 7, 13, 11, 8, 9, 9, 12, 15, 15, 4, 16, 9, 7, 9, 11, 10, 19, 8, 9, 10, 9, 10, 9, 16, 9, 12, 5, 15, 15, 8, 7, 8, 7, 12, 10, 10, 9, 9, 5, 8, 17, 6, 11, 9, 8, 14, 8, 18, 5, 11, 10, 7, 3, 11, 11, 9, 8, 12, 7, 10, 14, 9, 9, 10, 11, 14, 10, 14, 14, 8, 8, 6, 9, 10, 7, 7, 10, 12, 12, 14, 6, 17, 9, 10, 7, 321757, 14, 15, 14, 12, 15, 9, 8, 7, 10, 6, 10, 10, 7, 7422169, 9, 16, 12, 15, 5, 10, 14, 8, 6, 12, 9, 8, 9, 8, 7, 6, 9, 7, 7, 10, 5, 6, 9, 7, 9, 9, 9, 18, 15, 8, 9, 14, 8, 9, 10, 10, 9, 9, 8, 16, 13, 5, 10, 16, 7, 7, 9, 9, 9, 9, 10, 11, 12, 15, 9, 10, 11, 10, 10, 12, 9, 8, 8, 17, 14, 6, 10, 5, 8, 13, 8, 6, 11, 7, 6, 9, 8, 15, 12, 8, 9, 8, 7, 8, 7, 8, 15, 11, 15, 9, 7, 10, 16, 14, 4, 5, 8, 11, 9, 5, 6, 7, 16, 9, 6, 9, 7, 10, 10, 14, 9, 13, 10, 9, 9, 9, 7, 10, 7, 11, 6, 11, 8, 6, 10, 13, 8, 16, 7, 8, 10, 2, 8, 6, 4, 15, 12, 8, 13, 8, 17, 12, 18, 10, 10, 8, 9, 11, 16, 393923, 9, 7, 10, 10, 6, 7, 14, 10, 6, 9, 9, 16, 9, 6, 10, 8, 8, 36952, 5, 18, 11, 10, 7, 7, 4, 7, 10, 9, 8, 10, 8, 8, 11, 10, 10, 9, 11, 8, 7, 15, 11, 6, 7, 6, 8, 11, 9, 6, 8, 8, 7, 6, 13, 9, 8, 11, 10, 5, 9, 19, 10, 7, 11, 13, 4, 11, 10, 9, 8, 14, 11, 8, 7, 8}

Returns: {2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 8, 11, 14, 11, 8, 7, 10, 9, 7, 14, 1042528, 2, 14, 10, 13, 11, 9, 12, 4, 7, 16, 17, 13, 13, 10, 8, 18, 12, 14, 7, 6, 8, 11, 9, 11, 15, 9, 13, 11, 11, 7, 7, 17, 8, 15, 5, 7, 8, 6, 9, 9, 13, 15, 15, 13, 9, 14, 13, 9, 9, 9, 5, 7, 7, 13, 14, 12, 17, 13, 13, 7, 8, 10, 11, 14, 13, 7, 7, 6, 10, 8, 10, 10, 10, 9, 6, 12, 8, 11, 11, 9, 7, 14, 12, 9, 9, 8, 12, 10, 8, 17, 15, 5, 12, 15, 9, 11, 9, 9, 10, 14, 10, 5, 6, 8, 12, 9, 11, 7, 10, 13, 9, 9, 7, 9, 7, 13, 11, 10, 7, 7, 9, 9, 10, 9, 12, 13, 6, 9, 12, 9, 9, 8, 9, 7, 10, 9, 14, 6, 9, 10, 13, 7, 19, 11, 12, 11, 8, 4, 10, 10, 13, 9, 10, 10, 6, 16, 12, 14, 8, 10, 5, 7, 7, 4, 11, 11, 11, 15, 10, 12, 12, 14, 17, 6, 12, 13, 10, 8, 3, 9, 17, 8, 10, 10, 5, 11, 10, 12, 5, 5, 14, 7, 7, 9, 13, 7, 7, 8, 8, 19, 8, 11, 12, 13, 8, 8, 11, 8, 8, 10, 17, 12, 12, 8, 11, 7, 3, 10, 10, 7, 10, 4, 12, 9, 8, 7, 11, 7, 9, 11, 8, 11, 7, 16, 11, 13, 15, 6, 6, 10, 7, 7, 7, 9, 8, 12, 12, 12, 7, 6, 9, 11, 10, 10, 7, 13, 11, 17, 9, 9, 9, 4, 10, 9, 13, 13, 9, 7, 9, 10, 10, 10, 8, 11, 10, 9, 11, 10, 7, 9, 10, 11, 5, 11, 6, 17, 7, 13, 8, 6, 14, 10, 8, 8, 10, 10, 9, 9, 6, 13, 13, 7, 12, 13, 10, 15, 8, 7, 8, 8, 9, 13, 11, 7, 6, 9, 8, 6, 8, 12, 11, 18, 8, 11, 9, 8, 2, 10, 10, 5, 12, 6, 11, 7, 7, 8, 6, 10, 9, 6, 15, 9, 10, 9, 8, 10, 9, 11, 9, 10, 7, 6, 7, 7, 7, 7, 12, 13, 13, 9, 9, 10, 8, 8, 7, 8, 8, 11, 15, 7, 12, 7, 10, 9, 16, 8, 10, 9, 9, 9, 10, 9, 8, 19, 9, 9, 10, 13, 7, 12, 12, 13, 8, 15, 8, 7, 7, 6, 10, 11, 9, 8, 7, 12, 10, 6, 7, 8, 8, 11, 12, 7, 13, 10, 8, 11, 8, 11, 12, 9, 13, 9, 9, 14, 13, 10, 12, 13, 7, 9, 11, 7, 4, 12, 8, 7, 11, 7, 9, 9, 8, 13, 10, 6, 11, 18, 13, 14, 13, 12, 12, 9, 2, 10, 8, 11, 11, 8, 10, 6, 8, 8, 8, 8, 13, 8, 8, 7, 13, 7, 10, 17, 16, 7, 8, 6, 10, 10, 4, 8, 6, 13, 10, 9, 9, 11, 15, 11, 10, 11, 7, 13, 10, 8, 7, 11, 8, 8, 16601047, 9, 10, 10, 10, 11, 15, 13, 8, 9, 7, 9, 8, 10, 7, 13, 10, 14, 10, 15, 11, 13, 12, 9, 17, 6, 9, 18, 10, 19283719, 4, 10, 5, 9, 8, 17, 10, 10, 6, 13, 14, 7, 6, 10, 7, 11, 10, 10, 7, 8, 2, 8, 8, 5, 4, 19, 11, 9, 15, 7, 6, 11, 8, 7, 12, 6, 12, 10, 10, 11, 9, 10, 5, 6, 6, 7, 7, 10, 11, 4, 18, 7, 13, 10, 6, 12, 8, 6, 13, 11, 14, 6, 9, 11, 10, 8, 10, 11, 7, 11, 17, 15, 7, 8, 9, 12, 11, 8, 9, 5, 10, 9, 9, 10, 12, 8, 11, 9, 15, 9, 8, 12, 13, 11, 10, 7, 9, 11, 12, 8, 18, 10, 8, 16, 11, 10, 13, 10, 6, 14, 7, 6, 11, 16, 6, 11, 8, 4, 10, 9, 8, 9, 10, 10, 11, 16, 12, 10, 11, 9, 12, 9, 11, 14, 10, 7, 14, 11, 7, 9, 12, 9, 13, 12, 7, 9, 8, 6, 10, 8, 7, 9, 9, 13, 9, 9, 19, 10, 9, 8, 17, 13, 9, 8, 9, 8, 11, 5, 9, 7, 7, 9, 6, 18, 13, 7, 10, 9, 10, 11, 9, 11, 10, 10, 11, 10, 9, 11, 10, 13, 9, 8, 10, 9, 10, 9, 9, 7, 10, 10, 8, 10, 13, 7, 7, 11, 10, 14, 11, 13, 6, 13, 11, 9, 11, 13, 13, 9, 7, 7, 9, 6, 11, 6, 5, 13, 5, 10, 7, 12, 11, 10, 9, 13, 8, 6, 7, 14, 15, 9, 6, 9, 14, 13, 5, 7, 14, 10, 9, 7, 7, 15, 10, 6, 10, 17, 14, 11, 8, 4, 9, 10, 16, 19, 6, 13, 9, 9, 6, 9, 10, 18, 9, 8, 7, 12, 11, 9, 13, 14, 10, 6, 10, 12, 10, 9, 9, 8, 11, 12, 10, 7, 6, 10, 15, 11, 10, 8, 10, 14, 7, 7, 13, 8, 8, 13, 11, 7, 10, 10, 10, 12, 8, 8, 9, 10, 8, 14, 8, 15, 15, 12, 9, 12, 12, 7, 16, 9, 8, 8, 12, 11, 12, 10, 9, 6, 12, 8, 8, 9, 10, 12, 10, 13, 11, 11, 10, 7, 8, 7, 8, 10, 12, 6, 12, 12, 8, 7, 14, 12, 9, 6, 9, 8, 9, 9, 364429774, 9, 8, 6, 9, 8, 17, 9, 10, 4, 11, 13, 11, 12, 9, 4, 14, 8, 12, 5, 7, 15, 10, 13, 17, 11, 8, 6, 12, 18, 8, 10, 8, 9, 10, 5, 10, 10, 11, 11, 8, 8, 12, 12, 11, 10, 11, 16, 9, 10, 3, 13, 8, 12, 8, 9, 13, 9, 10, 18, 8, 8, 8, 13, 6, 7, 9, 8, 7, 12, 4, 14, 6, 8, 11, 14, 8, 9, 9, 13, 10, 4, 9, 7, 9, 11, 9, 6, 8, 9, 14, 7, 7}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{15, 7, 7, 8, 8, 10, 12, 9, 6, 74968869, 6, 8, 9, 6, 8, 11, 8, 14, 4, 6, 8, 6, 11, 7, 11, 7, 8, 6, 10, 9, 8, 11, 8, 11, 7, 10, 10, 13, 7, 6, 36182, 8, 3, 9, 9, 10, 8, 8, 9, 10, 12, 4, 9, 11, 10, 7, 5, 8, 9, 9, 9, 11, 9, 11, 10, 8, 759876, 8, 5, 12, 7, 6, 5, 6, 4, 11, 11, 8, 12, 8, 8, 7, 8, 5, 10, 6, 8, 8, 7, 8, 8, 7, 9, 8, 11, 7, 6, 12, 8, 11, 8, 7, 5, 13, 10, 16, 11, 8, 6, 8, 6, 3204, 10, 7, 8, 8, 10, 5, 7, 12, 8, 10, 14, 8, 9, 13, 6, 10, 6, 10, 8, 8, 10, 10, 5, 10, 9, 8, 5, 5, 6, 11, 14, 11, 15, 7, 10, 9, 11, 14, 10, 9, 7, 7, 15, 11, 8, 12, 10, 7, 7, 8, 7, 9, 7, 10, 14, 10, 10, 9, 12877614, 14, 11, 8, 9, 11, 14, 5, 8, 6, 15, 10, 5, 11, 6, 12, 10, 7, 14815, 8, 8, 9, 15, 8, 9, 4, 4, 9, 7, 8, 7, 8, 6, 9, 5, 9, 11, 7, 12, 7, 12, 9, 14, 7, 6, 8, 5, 9, 9, 11, 1294419, 7, 10, 11, 4, 15, 9, 10, 6, 6, 11, 11, 15318, 10, 7, 7, 6, 8117, 11, 10, 10, 4, 10, 9, 6, 10, 9, 7, 7, 3192124, 11, 10, 8, 12, 12, 8, 12, 8, 7, 10, 11, 12, 10, 8, 11, 10, 10, 7, 8, 12, 10, 10, 12, 7, 12, 11, 16, 9, 12, 10, 9, 7, 10, 11, 8, 9, 6, 9, 12, 7, 9, 13, 9, 9, 40626730, 10, 9, 13, 6, 7, 9, 8, 13, 8, 11, 10, 13, 4, 3, 7, 15, 10, 10, 10, 10, 6, 9, 11, 11, 9, 9, 11, 10, 11, 12, 15, 9, 8, 4, 11, 7, 7, 7, 6, 14, 13, 10, 6, 11, 14, 12, 5, 5, 11, 14, 13, 11, 7, 10, 9, 11, 8, 15, 13, 8, 11, 7, 7, 13, 15, 7, 8, 10, 25489227, 12, 6, 12, 12, 9, 6, 7, 9572254, 11, 14, 19049308, 11, 8, 8, 9, 6, 7, 10, 11, 6, 6, 7, 10, 12, 9, 10, 8, 6, 11, 6, 6, 6, 6, 10, 11, 11, 7, 5, 15, 10, 10, 10, 9, 12, 5, 7, 6, 10, 12, 9, 11, 6, 9, 11, 8, 10, 11, 10, 8, 21921, 683659, 6, 14, 13, 11, 11, 10, 7, 11, 8, 7, 6, 8, 6, 6, 2, 16, 10, 6, 8, 11, 6, 11, 9, 11, 12, 9, 11, 5, 13, 12, 5, 8, 11, 11, 7, 10, 8, 14, 9, 10, 6, 9, 10, 11, 12, 9, 1730, 7, 8, 9, 8, 8, 11, 5, 11, 91410905, 9, 10, 6, 6, 11, 3244686, 11, 10, 11, 7, 7, 4, 10, 6, 9, 11, 12, 11, 6314171, 13, 11, 13, 8, 493820190, 10, 7, 15, 817542, 8, 9, 5, 7, 15, 6, 13, 5908, 7, 7, 9, 8, 10, 11, 7, 11, 10, 6, 8, 10, 11, 7, 9, 12976355, 11, 10, 13, 8, 8, 9, 7, 7, 10, 10, 6, 10, 3, 11, 5, 15, 3, 11, 7, 12, 9, 7, 11, 7, 9, 10, 8, 7, 11, 11, 9, 15, 14, 6, 10, 459640892, 13, 8, 7378818, 6, 11, 11, 9, 12, 9, 11, 9, 10, 11, 6, 9, 6, 11, 10, 12, 15, 8, 8, 9, 9, 15, 10, 7, 7, 6, 11, 10, 11, 16, 9, 9, 6, 10, 15, 6, 7, 10, 5, 7, 8, 7, 14, 8, 9, 11, 10, 7, 10, 15, 13, 8, 6, 9, 11, 6, 8, 10, 15, 6, 12, 10, 9, 5, 10, 13, 12, 7, 10, 14, 9, 7, 12, 7, 9, 7, 10, 7, 9, 12, 13, 7, 11, 12, 9, 8, 6, 420458988, 11, 11, 8, 15, 8, 11, 9, 10, 7, 15, 10, 6, 13, 9, 28234, 7, 6, 9, 13, 11, 9, 8, 3038, 10, 6, 5, 7, 6, 9, 5, 10, 10, 7, 12718023, 5, 10, 5, 9, 6, 11, 12, 12, 7, 11, 9, 1949887, 8, 8, 7, 7, 16, 7, 6, 11, 6, 5, 6, 13, 14, 7, 6, 9, 10, 5, 7, 11, 7, 13, 5, 14, 6, 12, 7, 8, 7, 1162860, 11, 8, 8, 8, 12, 6, 6, 8, 15, 8, 14, 8, 8, 12, 8, 8, 5, 7, 9, 8, 12, 5, 3, 8, 14, 9, 10, 13, 10, 12, 8, 12, 8, 7, 4, 9, 9, 10, 10, 10, 10, 8, 9, 8, 268850, 8, 6, 7, 10, 13, 8, 6, 14, 10, 12, 13, 10, 4, 9, 7, 11, 10, 5, 7, 8, 10, 11, 7, 9, 10, 10, 14, 7, 9, 8, 9, 7, 10, 12, 10, 13, 15, 7, 6, 8, 11, 10, 11, 6, 8, 7, 11, 15, 11, 11, 9, 13, 16, 8, 7, 6, 11, 6, 6, 8, 8, 10, 9, 9, 11, 3, 9, 8, 7, 8, 11, 13, 10, 258729573, 7, 7, 11, 9, 7, 11, 9, 11, 9, 11, 10, 11, 10, 7, 7, 13, 11, 8, 5, 2, 7, 8, 6, 9, 12, 8, 9, 11, 10, 6, 6, 7, 12, 6, 6, 10, 10, 7, 10, 10, 11, 7, 8, 11, 4, 11, 6, 7, 8, 10, 11, 10, 9, 9, 6, 6, 7, 6, 9, 6, 10, 9, 11, 10, 8, 12, 9, 7, 10, 8, 8, 13, 6, 12, 8, 9, 13, 11, 6, 11, 981616, 10, 11, 8, 12, 10, 9, 6, 14, 9, 9, 8, 8, 6, 8, 4, 12, 10, 8, 13, 13, 9, 12, 7, 10, 12, 11, 9, 9, 6, 7, 9, 11, 9, 12, 10, 8, 12, 11, 9, 7, 7, 7, 5, 8, 11, 8, 11, 13, 11, 4}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 }
{11, 12, 9, 12, 9, 9, 16, 12, 13, 11, 10, 11, 12, 6, 12, 13, 10, 15, 12, 6, 11, 11, 11, 8, 15, 12, 12, 10, 11, 15, 10, 9, 15, 12, 4, 9, 5, 10, 13, 12, 11, 10, 1286800, 8, 7, 10, 6, 14, 10, 12, 12, 14, 9, 13, 12, 8, 11, 10, 11, 13, 10, 9, 9, 14, 8, 12, 14, 12, 6, 14, 10, 10, 10, 13, 11480, 14, 18, 9, 13, 7, 12, 12, 15, 13, 11, 10, 10, 11, 6, 10, 5, 10, 12, 10, 14, 12, 11, 11, 18, 8, 11, 11, 14, 5, 11, 10, 11, 16, 6, 10, 9, 11, 12, 9, 13, 9, 9, 14, 13, 7, 12, 10, 10, 14, 9, 5, 144907, 7, 8, 15, 11, 12, 6, 12, 3310, 12, 7, 10, 12, 11, 12, 10, 11, 11, 15, 11, 7, 8, 8, 6, 11, 11, 8, 12, 16, 7, 12, 13, 13, 5, 10, 7, 7, 8, 9, 12, 14, 8, 11, 12, 10, 13, 11, 11, 15, 13, 12, 11, 10, 9, 12, 14, 8, 9, 5, 15, 12, 13, 12, 13, 11, 14, 12, 13, 13, 11, 15, 8, 11, 13, 11, 7, 6, 13, 14, 13, 6, 8, 8, 14, 11, 18, 12, 6, 12, 8, 11, 2, 15, 10, 11, 9, 4, 7, 10, 9, 7, 12, 6, 13, 774962, 8, 12, 7, 12, 5, 15, 15, 5, 6, 13, 6, 8, 14, 12, 16, 5, 13, 15, 837101, 13, 12, 11, 8, 12, 11, 7, 10, 13, 13, 11, 4, 11, 10, 9, 11, 12, 12, 9, 13, 5, 15, 10, 14, 9, 14, 12, 10, 10, 9, 7, 10, 9, 13, 11, 7, 6, 9, 10, 12, 9, 10, 13, 8, 12, 6, 13, 3, 14, 9, 8, 11, 15, 11, 10, 12, 11, 10, 10, 13, 6, 7, 16, 7, 14, 11, 12, 15, 8, 12, 14, 16, 7, 12, 5, 10, 7, 11, 9, 10, 12, 8, 10, 11, 6, 12, 10, 10, 12, 14, 9, 9, 9, 15, 14, 8, 12, 9, 9, 9, 8, 5, 13, 14, 14, 12, 9, 10, 11, 6, 9, 10, 13, 12, 14, 13, 9, 16, 13, 10, 14, 10, 5, 9, 6, 13, 6, 11, 4, 12, 12, 10, 13, 11, 7, 8, 11, 11, 13, 131536718, 7, 8, 9, 16, 12, 12, 12, 10, 5, 14, 15, 11, 14, 11, 7, 13, 11, 11, 16, 16, 8, 14, 11, 12, 12, 4, 10, 13, 12, 7, 11, 9, 10, 9, 8, 11, 10, 12, 9, 10, 12, 11, 13, 10, 14, 11, 13, 13, 10, 12, 13, 10, 12, 6, 12, 9, 8, 15, 10, 10, 10, 6, 9, 7, 14, 12, 8, 9, 5, 6, 12, 12, 14, 5, 13, 12, 13, 4, 3, 12, 16, 9, 8, 13, 12, 15, 10, 13, 279719895, 264116532, 13, 9, 14, 4, 11, 15, 11, 12, 11, 10, 16, 14, 10, 9, 12, 9, 14, 14, 8, 13, 9, 10, 15, 12, 6, 14, 13, 11, 10, 5, 11, 7, 11, 528123042, 10, 10, 11, 12, 11, 12, 11, 12, 116678, 14, 13, 15, 11, 12, 11, 12, 11, 8, 9, 11, 10, 12, 12, 8, 14, 15, 12, 13, 8, 13, 4, 12, 12, 15, 13, 10, 16, 12, 11, 10, 4, 13, 11, 13, 179525, 7, 11, 14, 10, 12, 15, 13, 11, 7, 8, 8, 11, 12, 9, 12, 12, 11, 10, 10, 12, 14, 12, 12, 8, 6, 11, 12, 11, 12, 10, 13, 7, 12, 15, 12, 15, 11, 13, 12, 13, 12, 11, 11, 13, 11, 14, 9, 15, 14, 13, 12, 11, 13, 16, 15, 11, 12, 16, 13, 12, 10, 13, 14, 12, 6, 10, 8, 10, 8, 1242678, 10, 15, 12, 12, 14, 14, 11, 11, 10, 6, 11, 12, 11, 13, 12, 9, 14, 12, 12, 11, 10, 8, 8, 10, 12, 11, 11, 14, 14, 11, 9, 14, 10, 12, 14, 8, 13, 12, 15, 13, 12, 6, 12, 13, 13, 10, 15, 8, 11, 9, 8, 4967, 17, 5, 7, 12, 11, 11, 12, 11, 11, 11, 12, 8, 12, 12, 14, 11, 8, 7, 14, 14, 7, 13, 11, 11, 7, 12, 10, 11, 14, 15, 12, 4, 14, 13, 8, 11, 10, 11, 12, 9, 360108830, 12, 11, 13, 12, 7, 15, 8, 9, 9, 11, 14, 15, 5, 6, 12, 13, 12, 10, 15, 8, 14, 14, 5, 6, 10, 9, 13, 1, 12, 15, 7, 12, 7, 5, 6, 8, 11, 13, 11, 10, 11, 9, 11, 10, 9, 7, 13, 13, 11, 132645288, 11, 11, 7, 10, 14, 11, 12, 10, 7, 13, 9, 13, 12, 15, 12, 8, 2, 14, 8, 13, 13, 14, 7, 13, 13, 9, 8, 12, 12, 12, 13, 15, 8, 13, 14, 13, 14, 12, 14, 6, 13, 12, 10, 14, 255054, 12, 11, 16, 8, 10, 13, 13, 11, 17, 4, 10, 12, 12, 10, 12, 11, 14, 11, 13, 7, 8, 6, 32543, 9, 11, 6, 14, 8, 12, 13, 13, 14, 10, 5, 10, 13, 9, 13, 13, 15, 7, 8, 12, 10, 20954, 10, 14, 13, 9, 12, 2017, 8, 11, 7, 12, 12, 14, 6, 12, 12, 13, 5, 12, 12, 12, 8, 13, 12, 9, 10, 10, 11, 13, 9, 10, 9, 13, 14, 12, 11, 7, 15, 4, 16, 14, 6, 13, 15, 11, 12, 11, 16, 7, 33270753, 9, 12, 11, 40153148, 11, 7, 19827490, 13, 14, 5, 12, 10, 15, 2030050, 11, 13, 16, 15, 12, 17790760, 7, 7, 12, 13, 11, 13, 7, 3258, 8, 6, 2946883, 12, 12, 4, 12, 7, 15, 12, 8, 9, 12, 6, 13, 16, 5, 12, 13, 8, 15, 8, 12, 11, 16, 14, 11, 65411, 10, 9, 14, 14, 11, 14, 15, 12, 12, 9, 14, 6, 14, 12, 9, 11, 10, 42839, 16, 9, 13, 13, 13, 4, 14, 12, 11, 15, 16}

Returns: {-1 }
{13, 10, 10, 12, 8, 13, 12, 9, 9, 7, 11, 6, 8, 9, 8, 8, 9, 10, 12, 10, 5, 12, 8, 6, 10, 8, 10, 8, 6, 10, 10, 9, 6, 8, 9, 11, 9, 6, 10, 10, 7, 13, 13, 5, 10, 9, 2, 5, 8, 9, 10, 7, 7, 13, 8, 7, 10, 14, 10, 9, 4, 7, 10, 11, 11, 7, 8, 8, 13, 11, 13, 7, 9, 10, 7, 13, 6, 5, 6, 12, 12, 8, 8, 6, 10, 5, 6, 11, 6, 9, 10, 11, 10, 9, 8, 8, 7, 14, 11, 10, 7, 2, 9, 6, 8, 8, 7, 12, 7, 8, 10, 7, 10, 6, 5, 8, 8, 11, 10, 10, 13, 12, 7, 8, 11, 6, 10, 11, 13, 7, 13, 13, 2, 13, 7, 11, 9, 12, 4, 8, 9, 9, 13, 10, 10, 5, 10, 8, 9, 12, 11, 5, 12, 4, 9, 8, 11, 9, 7, 12, 11, 11, 9, 7, 12, 9, 5, 10, 12, 6, 12, 11, 13, 10, 8, 10, 6, 6, 11, 8, 10, 8, 10, 9, 9, 4, 11, 10, 10, 10, 5, 9, 9, 11, 6, 10, 13, 9, 5, 10, 9, 6, 9, 12, 11, 10, 6, 9, 6, 10, 11, 9, 11, 6, 4, 13, 8, 6, 12, 13, 12, 6, 7, 8, 4, 5, 5, 11, 14, 7, 12, 6, 10, 5, 12, 14, 9, 12, 6, 9, 11, 11, 12, 9, 4, 13, 10, 8, 9, 12, 10, 9, 14, 10, 10, 8, 12, 10, 8, 8, 7, 7, 10, 8, 8, 12, 12, 7, 9, 7, 14, 10, 8, 12, 11, 8, 3, 12, 7, 10, 8, 9, 8, 13, 5, 11, 10, 10, 10, 5, 10, 12, 9, 10, 13, 11, 9, 10, 9, 14, 7, 11, 11, 8, 10, 4, 13, 11, 5, 5, 9, 7, 14, 11, 7, 11, 9, 8, 10, 8, 13, 14, 6, 9, 8, 5, 9, 11, 6, 13, 12, 9, 13, 10, 4, 11, 7, 7, 8, 11, 9, 7, 10, 11, 13, 7, 6, 13, 10, 4, 11, 6, 13, 15, 12, 8, 6, 11, 10, 9, 13, 9, 10, 10, 4, 5, 10, 13, 6, 7, 8, 9, 8, 8, 12, 9, 8, 9, 9, 7, 5, 11, 7, 10, 10, 10, 6, 14, 9, 6, 8, 11, 5, 11, 7, 12, 12, 8, 10, 10, 12, 8, 7, 10, 8, 7, 9, 10, 14, 7, 7, 8, 13, 7, 12, 9, 9, 9, 7, 10, 7, 7, 9, 13, 6, 12, 5, 9, 12, 10, 11, 11, 11, 11, 12, 8, 13, 10, 14, 9, 10, 7, 11, 13, 7, 9, 13, 13, 12, 14, 9, 10, 10, 12, 10, 8, 9, 5, 8, 14, 8, 9, 12, 10, 10, 9, 5, 11, 14, 7, 9, 10, 8, 5, 8, 10, 8, 12, 10, 10, 9, 8, 11, 8, 12, 8, 5, 13, 6, 11, 6, 11, 11, 5, 9, 6, 8, 10, 4, 15, 8, 9, 11, 10, 11, 7, 12, 9, 11, 10, 7, 11, 9, 12, 8, 10, 9, 7, 7, 8, 10, 10, 11, 5, 10, 9, 3, 10, 11, 11, 10, 8, 10, 14, 15, 9, 10, 6, 8, 8, 6, 13, 7, 13, 9, 9, 7, 9, 10, 10, 12, 8, 10, 14, 8, 8, 9, 13, 9, 6, 6, 9, 11, 8, 13, 8, 9, 12, 12, 9, 7, 6, 9, 11, 12, 7, 9, 9, 12, 7, 9, 9, 12, 5, 5, 6, 12, 12, 5, 9, 10, 12, 11, 11, 7, 9, 11, 13, 5, 11, 11, 11, 9, 7, 8, 10, 9, 9, 6, 10, 9, 13, 6, 4, 9, 11, 10, 7, 6, 7, 9, 12, 14, 8, 10, 10, 8, 11, 8, 8, 7, 10, 9, 10, 10, 10, 12, 10, 9, 11, 9, 10, 13, 12, 9, 11, 11, 8, 9, 10, 8, 7, 8, 6, 10, 8, 8, 6, 9, 3, 9, 124862, 9, 8, 7, 7, 11, 8, 10, 6, 8, 7, 11, 7, 10, 10, 8, 8, 9, 7, 12, 4, 13, 13, 10, 9, 11, 13, 8, 13, 7, 8, 12, 9, 7, 12, 7, 10, 7, 10, 11, 9, 9, 9, 6, 8, 9, 14, 8, 13, 10, 8, 9, 9, 9, 5, 14, 6, 8, 9, 6, 12, 13, 9, 7, 12, 9, 7, 8, 8, 11, 10, 12, 9, 12, 13, 8, 6, 14, 6, 8, 6, 5, 12, 11, 11, 12, 8, 12, 8, 5, 9, 8, 7, 15, 10, 6, 9, 12, 10, 7, 10, 10, 8, 8, 8, 10, 7, 8, 10, 13, 6, 8, 9, 6, 8, 12, 9, 11, 8, 10, 10, 7, 7, 10, 8, 6, 8, 9, 7, 10, 13, 9, 10, 8, 9, 7, 6, 10, 5, 10, 13, 11, 11, 10, 12, 4, 13, 8, 9, 6, 12, 9, 14, 9, 10, 8, 12, 13, 13, 9, 10, 5, 10, 13, 10, 6, 10, 6, 11, 12, 12, 9, 8, 11, 13, 12, 7, 9, 8, 8, 8, 9, 9, 8, 11, 12, 10, 8, 8, 9, 10, 6, 9, 6, 7, 12, 8, 10, 13, 13, 10, 6, 9, 6, 7, 11, 9, 10, 10, 15, 11, 10, 11, 8, 14, 11, 7, 9, 7, 12, 11, 6, 12, 9, 7, 14, 7, 13, 7, 10, 13, 7, 10, 5, 13, 8, 8, 9, 10, 14, 10, 7, 7, 10, 6, 9, 8, 12, 10, 10, 10, 9, 6, 8, 10, 7, 7, 7, 6, 6, 11, 10, 7, 10, 8, 7, 7, 11, 8, 9, 6, 9, 13, 7, 7, 10, 6, 14, 10, 13, 9, 12, 5, 10, 8, 5, 8, 8, 11, 8, 10, 7, 10, 10, 6, 9, 8, 12, 12, 9, 9, 7, 7, 8, 8, 10, 8, 14, 10, 11, 12, 9, 10, 7, 9, 8, 13, 8, 13, 10, 10, 15, 9, 9, 5, 7, 9, 14, 9, 4, 9, 8, 7, 10, 10, 10, 8, 10, 9}

Returns: {-1 }
{6, 8, 9, 9, 11, 8, 10, 12, 8, 11, 7, 17993, 10, 10, 5, 13, 11, 13, 9, 11, 5, 1507, 9, 12, 9, 8, 5, 10, 8, 6, 9, 7, 5, 6, 9, 9, 7, 9, 9, 10, 6, 8, 9, 11, 7, 9, 10, 11, 10, 12, 8, 7, 5, 228302, 10, 9, 11, 12, 8, 11, 5, 11, 6, 5, 8, 5, 26530410, 17425858, 9, 10, 12, 6, 12, 11, 12, 245880824, 9, 10, 3, 6, 49221619, 10, 8, 10, 12, 7, 5, 10, 8, 9, 9, 4, 11, 10, 11, 2, 8, 5, 6, 10, 8, 8, 7, 6, 6, 9, 6, 11, 11, 8, 8, 11, 12, 7, 7, 6, 8, 13, 9, 6, 7, 4, 11, 11, 8, 9, 7, 8, 8, 10, 12, 9, 9, 8, 11, 12, 9, 5, 5, 11, 6, 5, 5, 8, 8, 5, 8, 10, 5, 10, 8, 9, 11468, 8, 64754, 13, 6, 9, 8, 5, 31218, 11, 9, 12, 8, 5, 8, 12, 11, 5, 10, 6, 9, 10, 9, 5, 6, 9, 6, 6, 9, 11, 9, 5, 11, 12, 9, 8, 7, 6, 5, 12, 11, 10, 9, 7, 11, 8, 8, 4, 12, 11, 7, 7, 8957, 9, 8, 7, 7, 8, 9, 9, 10, 5, 8, 10, 10, 10, 10, 7, 11, 8, 10, 6, 8, 6, 8, 4, 11, 8, 13, 3, 7, 3015253, 7, 8, 7, 12, 7, 8, 13, 6, 8, 9, 9, 9, 12, 6, 9, 10, 10, 11, 9, 62291879, 8, 9, 10, 11, 14, 10, 10, 11, 8, 8, 9, 8, 9, 9, 6, 5, 166951, 7, 12, 10, 9, 7, 10, 4, 511467464, 11, 10, 10, 10, 7, 8, 6, 10, 9, 8, 7, 5, 8, 7, 9, 4, 9, 7, 11, 7, 9, 8, 11, 9, 7, 10, 9, 5, 9, 7, 6, 9, 8, 8, 8, 10, 9, 12, 8, 10, 5, 9, 9, 8, 10, 258721, 9, 9, 11, 6, 6, 8, 9, 35255561, 11, 11, 11, 10, 6, 10, 10, 9, 9, 5, 8, 11, 11, 9, 9, 6, 12, 10, 10, 12, 9, 9, 8, 9, 7, 9, 9, 12, 7, 1609, 7, 9, 8, 8, 11, 7, 6, 4, 11, 10, 8, 7, 9, 4, 8, 10, 9, 9, 11, 9, 10, 8, 10, 10, 4237, 11, 11, 9, 8, 8, 5, 7, 5, 8, 7, 11, 11, 7, 9, 8, 7, 9, 4, 9, 8, 10, 8, 7, 9, 7, 6, 8, 9, 10, 8, 9, 9, 13, 10, 6, 7, 11, 6, 7, 10, 11, 11, 10, 9, 9, 10, 7, 13, 7990, 383222, 10, 9, 11, 11, 6, 6, 11, 8, 4, 8, 9, 994324, 7, 10, 10, 49344399, 9, 8, 11, 8, 6, 11, 3, 5, 9, 8, 13, 8, 7, 6, 5, 9, 8, 10, 9, 10, 7, 6, 6, 9, 265794024, 2840, 9, 9, 4778584, 4, 4, 9, 9, 7, 10, 9, 3623774, 4, 7, 11, 10, 6808113, 9, 10, 9, 10, 10, 9, 6, 12, 6, 9, 13, 8, 9, 8, 3, 13, 7, 7, 9, 12, 7, 9, 7, 11, 8, 7, 11, 10, 9, 11, 7, 10, 9, 13, 5, 8, 9, 8, 11, 7, 11, 11, 7, 10, 9, 9, 10, 8, 10, 13, 9, 5, 9, 10, 10, 9, 8, 10, 7, 9, 8, 8, 5, 5, 11, 11, 8, 10, 1239, 6, 9, 13, 9, 8, 10, 6, 8, 10, 8, 11, 5, 8, 7, 11, 10, 12, 6, 7, 7, 9, 9, 8, 10, 11, 11, 9, 8, 11, 8, 7, 11, 5, 7, 8, 11, 8, 10, 5, 11, 6, 10, 9, 6, 10, 6, 9, 8, 7, 8, 7, 11, 9, 8, 11, 12, 5, 9, 9, 10, 9, 8, 5, 8, 8, 8, 9, 12, 5, 5, 8, 10, 10, 7, 13, 11, 8, 12, 10, 9, 9, 13, 11, 11, 14, 10, 10, 9, 8, 10, 11, 8, 7, 6, 10, 11, 6, 5, 8, 8, 11, 7, 11, 11, 11, 9, 7, 11, 7, 8, 5, 11, 11, 3536980, 3312040, 5, 8, 6, 5, 13, 11, 7, 10, 8, 6, 11, 9, 10, 5, 5, 9, 9, 8, 11, 13, 5, 10, 9, 9, 652715, 7, 10, 10, 10, 8, 9, 7, 9, 7, 7, 11, 7, 5, 8, 85519, 11, 8, 10, 5, 11, 8, 5, 7, 10, 8, 11, 10, 6, 12, 11, 6, 5, 10, 6, 8, 9, 10, 5, 7, 5, 7, 7, 10, 8, 10, 8, 9, 10, 11, 9, 9, 12, 11, 11, 10, 9, 12, 8, 2277910, 11, 6, 6, 7, 4, 10, 9, 5, 12, 10, 4, 9, 6, 1509, 9, 8, 11, 4, 13, 11, 10, 7302, 9, 5, 7, 8, 8, 6, 5, 7, 10, 8, 8, 7, 10, 10, 10, 10, 12, 10, 5, 7, 8, 9, 11, 8, 7, 6, 10, 6464047, 9, 11, 11, 7, 8, 6, 9, 10, 8, 10, 8, 13, 11, 8, 9, 12, 8, 10, 8, 8, 9, 10, 10, 9, 9, 10, 39469712, 8, 10, 11, 9, 7, 8, 6, 7, 5, 353142774, 7, 7, 8, 10, 6, 8, 5, 7, 9, 13, 8, 7, 11, 10, 10, 10, 13, 10, 8, 8, 8, 8, 10, 6, 5, 6, 10, 6, 12, 8, 10, 10, 14, 11, 7, 8, 9, 5, 10, 7, 9, 12, 5, 11, 9, 8, 8, 9, 11, 6, 10, 10, 5, 9, 7, 6, 592397, 9, 515530922, 8, 5, 11, 5, 8, 13, 8, 8, 8, 6, 7, 7, 8, 8, 9, 9, 6, 5, 13, 7, 8, 11, 5, 7, 6, 13, 9, 10, 6, 9, 10, 11, 6, 12, 102303008, 9, 6, 7, 10, 9, 7, 7, 9, 7, 9, 12, 8, 9, 7, 9, 8, 8, 5, 6, 9, 5, 6, 7, 10, 6, 5, 5, 6, 8, 6, 5, 7, 6, 8, 11, 11, 12, 11, 12, 9, 8, 13, 12, 4410183, 3, 8, 9}

Returns: {-1 }
{9, 9, 12, 9, 9, 9, 10, 9, 7, 8, 6, 8, 9, 9, 9, 10, 9, 11, 9, 11, 6, 8, 13, 8, 7, 10, 7, 7, 13, 9, 8, 8, 7, 9, 8, 6, 10, 8, 8, 7, 8, 10, 7, 9, 8, 9, 10, 8, 9, 6, 9, 9, 10, 12, 9, 8, 11, 12, 10, 8, 6, 9, 15, 10, 9, 8, 3, 9, 9, 8, 10, 8, 5, 11, 9, 11, 8, 372372, 9, 12, 9, 9, 7, 11, 11, 7, 6, 9, 6, 10, 12, 10, 14, 14, 6, 10, 7, 10, 12, 8, 9, 9, 7, 11, 10, 8, 9, 13, 7, 10, 12, 6, 10, 11, 9, 10, 7, 8, 8, 9, 10, 11, 6, 5, 8, 9, 8, 9, 7, 10, 10, 7, 7, 8, 6, 10, 7, 9, 7, 8, 8, 10, 12, 9, 8, 9, 9, 10, 7, 7, 11, 8, 7, 11, 14, 13, 9, 9, 13, 5, 7, 6, 11, 10, 7, 10, 9, 11, 7, 11, 9, 5, 15, 11, 10, 11, 7, 9, 9, 9, 10, 8, 10, 8, 7, 8, 11, 4, 4, 9, 9, 10, 9, 9, 8, 6, 9, 11, 7, 8, 5, 10, 7, 6, 9, 10, 10, 8, 8, 4, 8, 10, 8, 6, 4, 8, 7, 8, 7, 10, 10, 8, 6, 10, 4, 12, 7, 7, 10, 8, 9, 5, 12, 7, 7, 10, 7, 8, 6, 5, 9, 7, 9, 9, 8, 9, 9, 8, 10, 10, 10, 14, 10, 10, 9, 10, 10, 8, 8, 8, 11, 8, 11, 10, 11, 7, 9, 6, 10, 10, 8, 9, 7, 9, 8, 12, 8, 11, 8, 9, 10, 11, 10, 7, 7, 8, 10, 12, 4, 6, 10, 12, 9, 10, 7, 10, 7, 6, 14, 8, 9, 5, 12, 8, 4, 9, 8, 7, 8, 9, 11, 10, 11, 9, 7, 7, 12, 10, 10, 9, 11, 7, 6, 7, 8, 6, 8, 8, 8, 7, 11, 10, 9, 10, 8, 6, 9, 9, 13, 5, 10, 10, 10, 10, 11, 10, 8, 9, 9, 8, 9, 9, 8, 9, 9, 8, 10, 10, 9, 9, 9, 7, 8, 9, 8, 4, 10, 13, 10, 7, 8, 6, 9, 8, 8, 15, 7, 9, 6, 7, 11, 10, 8, 8, 8, 9, 7, 5, 11, 14, 393985, 15, 8, 10, 9, 10, 9, 9, 8, 8, 9, 8, 5, 11, 8, 7, 2, 5, 9, 10, 8, 6, 8, 9, 8, 6, 11, 8, 8, 7, 6, 10, 13, 12, 8, 10, 6, 7, 8, 8, 10, 9, 8, 4, 6, 7, 6, 11, 6, 9, 6, 5, 8, 13, 7, 7, 4, 7, 8, 5, 5, 9, 7, 10, 9, 8, 9, 7, 10, 8, 9, 7, 4994456, 7, 11, 6, 8, 5, 10, 11, 8, 5, 7, 11, 7, 10, 8, 9, 8, 11, 9, 8, 11, 9, 10, 9, 5, 8, 9, 11, 8, 9, 9, 9, 9, 6, 6, 7, 7, 8, 9, 10, 10, 9, 3, 15, 7, 10, 7, 9, 10, 7, 9, 6, 8, 11, 9, 6, 8, 8, 11, 8, 10, 9, 15, 8, 7, 8, 8, 11, 3, 7, 7, 8, 2, 11, 9, 10, 8, 7, 7, 10, 9, 9, 9, 10, 8, 2, 9, 8, 6, 9, 8, 9, 7, 10, 9, 9, 8, 10, 9, 9, 14, 5, 9, 15, 10, 11, 10, 10, 7, 9, 11, 7, 13, 10, 7, 7, 8, 12, 9, 11, 5, 10, 9, 12, 8, 7, 8, 12, 6, 8, 7, 7, 5, 8, 8, 9, 7, 8, 7, 11, 12, 6, 7, 11, 10, 9, 10, 6, 8, 8, 7, 8, 11, 7, 8, 9, 6, 9, 6, 9, 10, 9, 8, 5, 6, 7, 7, 4, 8, 8, 6, 10, 10, 6, 13, 10, 8, 9, 9, 5, 10, 10, 14, 9, 8, 7, 10, 10, 7, 8, 7, 7, 8, 8, 13, 8, 6, 11, 9, 10, 10, 8, 7, 8, 7, 7, 8, 10, 13, 10, 6, 11, 8, 8, 9, 10, 9, 6, 9, 11, 7, 7, 9, 8, 8, 11, 6, 14, 10, 10, 7, 9, 11, 9, 10, 10, 8, 12, 15, 8, 8, 10, 8, 9, 10, 8, 6, 7, 11, 7, 7, 9, 8, 9, 10, 11, 9, 8, 5, 5, 9, 10, 7, 5, 9, 6, 3800306, 13, 7, 5, 10, 10, 8, 8, 10, 10, 10, 8, 12, 7, 10, 6, 11, 5, 4, 13, 8, 5, 8, 8, 9, 5105, 9, 7, 8, 8, 10, 8, 7, 9, 7, 9, 3, 7, 12, 9, 8, 9, 9, 10, 10, 8, 8, 9, 13, 8, 8, 7, 7, 9, 10, 8, 11, 9, 11, 4, 6, 13, 7, 12, 7, 7, 9, 6, 10, 9, 8, 10, 6, 11, 9, 9, 11, 8, 6, 11, 11, 7, 12, 9, 11, 8, 8, 11, 10, 14, 9, 10, 10, 14, 10, 6, 13, 12, 8, 12, 9, 8, 5, 7, 10, 7, 6, 5, 9, 10, 8, 10, 7, 10, 7, 8, 11, 13, 4, 9, 6, 9, 10, 9, 10, 7, 8, 7, 10, 10, 8, 8, 12, 9, 9, 11, 9, 10, 8, 10, 9, 10, 9, 6, 8, 9, 11, 12, 10, 8, 8, 9, 9, 10, 8, 5, 8, 11, 10, 8, 7, 8, 12, 7, 9, 6, 9, 11, 9, 9, 5, 8, 11, 10, 9, 8, 8, 9, 9, 9, 9, 10, 7, 12, 11, 9, 10, 9, 13, 7, 8, 8, 6, 10, 7, 10, 7, 9, 10, 11, 9, 7, 8, 10, 10, 8, 7, 5, 6, 15, 8, 9, 14, 8, 9, 9, 7, 9, 9, 9, 9, 10, 12, 7, 8, 5, 7, 9, 10, 9, 11, 9, 9, 10, 8, 10, 13, 7, 13, 12, 8, 9, 8, 9, 9, 7, 9, 10, 11, 8, 7, 9, 9, 8, 7, 10, 9, 8, 8, 8, 9, 8, 11, 7, 11, 11, 11, 9, 11, 8, 11, 5}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{7, 7, 10, 11, 8, 7, 6, 5, 10, 6, 11, 6, 10, 12, 11, 9, 9, 9, 7, 9, 9, 8, 6, 10, 13, 4, 10, 7, 10, 11, 10, 5, 10, 10, 10, 10, 10, 6, 9, 9, 8, 6, 6, 10, 11, 15, 8, 5, 8, 5, 8, 9, 6, 5, 8, 11, 10, 8, 15, 12, 5, 8, 10, 9, 12, 4, 10, 13, 7, 14, 10, 11, 6, 8, 10, 7, 7, 8, 9, 11, 13, 5, 8, 8, 10, 10, 6, 5, 15, 9, 12, 9, 7, 13, 12, 8, 11, 6, 9, 9, 12, 6, 10, 4, 12, 7, 12, 9, 12, 12, 10, 10, 10, 10, 9, 9, 9, 8, 8, 9, 3, 11, 13, 7, 10, 9, 10, 9, 9, 10, 13, 7, 11, 9, 7, 11, 9, 10, 6, 6, 11, 9, 14, 6, 10, 7, 12, 15, 9, 9, 7, 10, 8, 7, 8, 5, 10, 6, 8, 12, 10, 4, 9, 6, 14, 13, 9, 9, 8, 11, 7, 9, 12, 13, 9, 9, 8, 6, 13, 12, 7, 10, 10, 9, 6, 9, 7, 14, 11, 8, 10, 5, 7, 6, 13, 7, 9, 9, 15, 9, 10, 14, 10, 8, 5, 12, 11, 8, 12, 8, 6, 12, 8, 9, 9, 10, 10, 14, 8, 6, 6, 13, 14, 8, 13, 4, 10, 11, 13, 7, 10, 9, 9, 8, 11, 12, 10, 11, 10, 7, 10, 11, 11, 6, 13, 5, 7, 8, 10, 9, 5, 9, 12, 6, 7, 12, 9, 7, 10, 9, 10, 12, 11, 8, 11, 9, 12, 7, 10, 10, 12, 9, 10, 11, 10, 9, 7, 8, 9, 8, 11, 10, 10, 8, 9, 6, 11, 9, 9, 12, 4, 6, 8, 11, 10, 11, 16, 10, 5, 6, 6, 9, 5, 7, 14, 8, 14, 11, 13, 10, 8, 14, 8, 12, 10, 10, 11, 8, 7, 10, 7, 7, 5, 3, 14, 11, 13, 8, 10, 11, 12, 5, 13, 8, 7, 8, 3, 12, 5, 6, 12, 8, 9, 12, 8, 9, 9, 11, 8, 14, 12, 7, 11, 11, 9, 11, 8, 12, 9, 8, 8, 10, 4, 5, 12, 11, 12, 9, 4, 8, 10, 10, 12, 12, 7, 8, 5, 10, 6, 10, 8, 6, 14, 11, 11, 7, 13, 10, 11, 13, 10, 9, 13, 8, 14, 4, 13, 6, 9, 7, 8, 10, 8, 3, 7, 13, 7, 13, 9, 5, 13, 10, 8, 11, 13, 5, 7, 14, 10, 11, 10, 7, 13, 8, 13, 12, 9, 9, 6, 7, 7, 10, 14, 10, 10, 8, 8, 10, 8, 13, 9, 6, 10, 7, 35677176, 9, 14, 9, 13, 7, 7, 8, 12, 10, 10, 11, 8, 11, 11, 6, 5, 10, 8, 5, 10, 4, 11, 5, 8, 7, 9, 13, 9, 10, 9, 7, 8, 9, 7, 4, 5, 9, 9, 11, 11, 9, 7, 8, 13, 7, 5, 7, 7, 10, 5, 11, 8, 8, 13, 12, 8, 4, 8, 7, 9, 12, 8, 10, 10, 11, 12, 9, 12, 13, 8, 10, 13, 8, 11, 11, 5, 5, 11, 7, 10, 7, 6, 9, 9, 8, 8, 3, 13, 8, 9, 8, 8, 6, 9, 8, 12, 5, 12, 6, 9, 12, 8, 8, 8, 12, 11, 14, 10, 8, 6, 11, 13, 6, 9, 7, 5, 10, 8, 8, 6, 5, 6, 11, 10, 8, 13, 9, 12, 12, 5, 10, 9, 11, 8, 9, 13, 6, 8, 6, 6, 13, 10, 10, 5, 11, 11, 9, 12, 7, 12, 8, 4, 11, 7, 8, 9, 8, 7, 9, 11, 14, 8, 8, 7, 5, 7, 8, 14, 10, 8, 8, 12, 12, 5, 10, 11, 9, 7, 12, 8, 8, 11, 12, 11, 18472015, 9, 5, 11, 8, 10, 6, 14, 10, 10, 8, 9, 9, 13, 7, 4, 4, 10, 8, 8, 7, 9, 11, 10, 5, 12, 8, 7, 12, 10, 11, 10, 11, 6, 7, 11, 14, 9, 7, 11, 11, 6, 7, 8, 13, 9, 5, 9, 7, 8, 5, 3, 5, 7, 5, 11, 7, 6, 5, 11, 13, 9, 7, 6, 7, 8, 12, 11, 11, 6, 11, 12, 6, 8, 8, 5, 5, 9, 8, 9, 7, 16, 12, 9, 11, 240049485, 13, 11, 13, 9, 10, 7, 8, 5, 6, 8, 11, 5, 13, 7, 14, 8, 12, 7, 5, 12, 13, 14, 16, 6, 8, 12, 7, 7, 10, 5, 11, 11, 11, 9, 13, 10, 9, 8, 6, 12, 10, 8, 10, 10, 10, 11, 14, 10, 8, 7, 10, 13, 8, 8, 5, 7, 10, 12, 8, 13, 7, 9, 10, 10, 10, 10, 8, 8, 12, 7, 3, 11, 13, 8, 8, 12, 11, 9, 13, 11, 13, 10, 7, 9, 11, 8, 6, 11, 7, 14, 11, 11, 12, 6, 8, 4, 11, 8, 6, 13, 11, 13, 9, 9, 8, 9, 7, 5, 8, 14, 9, 8, 14, 8, 9, 13, 12, 5, 10, 12, 13, 6, 8, 10, 5, 6, 9, 10, 9, 11, 10, 7, 9, 9, 4, 9, 13, 3, 6, 13, 7, 7, 6, 9, 9, 4, 8, 10, 11, 5, 10, 8, 11, 7, 10, 15, 11, 9, 7, 3, 12, 7, 9, 9, 9, 7, 10, 8, 10, 10, 8, 11, 4, 10, 10, 8, 12, 10, 8, 10, 9, 14, 8, 10, 15, 7, 8, 8, 10, 8, 6, 8, 6, 10, 8, 15, 7, 5, 10, 11, 9, 10, 12, 7, 10, 5, 5, 7, 8, 13, 10, 8, 7, 12, 13, 6, 6, 8, 13, 14, 8, 7, 6, 8, 12, 6, 10, 7, 12, 13, 7, 11, 12, 12, 10, 7, 7, 8, 5, 6, 10, 12, 9, 9, 7, 13, 5, 7, 9, 11, 5, 7, 10, 12, 9, 7, 12, 12, 10, 13, 10, 8, 9, 8, 6, 10, 8, 9, 11, 10, 11, 11, 6}

Returns: {2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{11, 9, 7, 9, 11, 7, 7, 9, 7, 7, 8, 7, 9, 8, 10, 8, 6, 15, 11, 10, 6, 6, 8, 4, 12, 12, 11, 7, 11, 6, 9, 6, 8, 12, 15, 7, 5, 11, 8, 9, 7, 13, 9, 6, 3, 7, 11, 10, 11, 8, 3, 6, 12, 10, 7, 12, 12, 10, 10, 4274, 12, 8, 8, 7, 8, 3, 12, 7, 6, 8, 11, 6, 9, 10, 13, 15, 10, 5, 11, 8, 11, 10, 7, 10, 10, 10, 11, 13, 10, 12, 12, 7, 12, 12, 15, 6, 9, 6, 10, 9, 13, 5, 9, 8, 9, 9, 14, 5, 8, 9, 8, 10, 10, 7, 8, 7, 7, 2917212, 9, 12, 8, 9, 7, 11, 9, 80402616, 9, 7, 10, 14, 9, 13, 5, 10, 6, 836838, 10, 7, 9, 1044344, 5, 8, 13, 10, 9, 58797631, 6, 11, 2, 8, 10, 12, 5, 12, 5, 9, 12, 16, 8, 8, 9, 11, 9, 8, 11, 6, 10, 13, 7, 10, 7, 12, 13, 7, 9, 11, 5, 11, 11, 12, 9, 8, 9, 4, 12, 10, 13, 5, 11, 16, 30245, 11, 7, 7, 9, 11, 8, 10, 10, 9, 7, 12, 13, 14, 8, 11, 10, 7, 13, 4, 8, 6, 8, 10, 10, 6, 5, 10, 11, 9, 15, 11, 10, 7, 12, 12, 7, 12, 9, 8, 9, 8, 12, 10, 2, 8, 10, 7, 12, 9, 5, 12, 10, 8, 16, 14, 13, 7, 7, 9, 13, 9, 11, 9, 11, 10, 11, 14, 8, 11, 7, 9, 8, 6, 5, 8, 8, 10, 7, 8, 10, 6, 11, 5, 7, 10, 8, 10, 8, 10, 11, 8, 13, 7, 10, 7, 7, 11, 12, 12, 10, 10, 22833, 8, 12, 10, 7, 11, 8, 9, 10, 14, 9, 9, 11, 5, 13, 8, 12, 8, 10, 8, 10, 7, 8, 9, 7, 12, 12, 10, 13, 8, 10, 9, 8, 11, 7, 10, 7, 8, 11, 12, 8, 7, 9, 6, 7, 11, 7, 9, 12, 8, 7, 8, 14, 7, 9, 12, 8, 8, 6, 10, 9, 6, 14, 14, 8, 6, 12, 10, 9, 9, 10, 4, 12, 10, 14, 7, 13, 7, 7, 4, 9, 11, 10, 9, 11, 7, 6, 4, 11, 8, 3, 8, 15, 6, 7, 13, 11, 11, 392041401, 8, 7, 11, 11, 9, 11, 8, 11, 7, 8, 10, 5, 6, 8, 9, 14, 10, 11, 8, 8, 9, 7, 8, 11, 11, 11, 11, 5, 10, 10, 6, 6, 11, 13, 5, 10, 6, 5, 9, 7, 15, 7, 11, 10, 7, 10, 11, 9, 11, 5, 6, 5, 12, 11, 8, 13, 5, 9, 9, 10, 5, 6, 9, 11, 10, 7, 8, 7, 9, 8, 8, 8, 4, 11, 87707, 6, 5, 6, 9, 7, 10, 9, 11, 8, 14, 10, 8, 9, 7, 8, 12, 11, 8, 10, 7, 7, 10, 10, 8, 6, 9, 16, 9, 7, 7, 9, 5, 9, 6, 15, 12, 9, 5, 6, 20442, 16, 11, 9, 8, 6, 13, 9, 8, 12, 9, 11, 9, 10, 8, 8, 14, 8, 7, 10, 8, 15, 12, 9, 7, 10, 7, 11, 10, 12, 5, 10, 7, 14, 11, 7, 10, 7, 9, 5, 11, 11, 13, 12, 12, 12, 6, 28258, 7, 9, 11, 9, 7, 11, 8, 8, 13, 11, 16, 9, 11, 3956894, 6, 11, 8, 10, 10, 8, 10, 11, 14, 11, 10, 8, 7, 14, 13, 13, 13, 7, 14, 9, 11, 8, 8, 10, 7, 9, 8, 13, 8, 8, 7, 10, 11, 7, 5, 6, 10, 9, 2, 9, 10, 8, 11, 9, 6, 12, 9, 8, 10, 9, 12, 9, 9, 7, 9, 5, 10, 11, 9, 7, 12, 6, 11, 10, 4, 6, 8, 6, 6, 7, 8, 6, 12, 9, 7, 8, 12, 8, 8, 9, 11, 12, 10, 14, 9, 7, 7, 11, 11, 9, 9, 12, 11, 10, 10, 10, 13, 10, 8, 6, 10, 11, 8, 12, 6, 6, 8, 4, 3852, 5, 9, 8, 10, 9, 8, 11, 427157507, 8, 8, 12, 6, 7, 7, 5, 11, 11, 9, 6, 12, 14, 10, 5, 6, 8, 6, 11, 10, 13, 8, 8, 6, 10, 6, 5, 9, 8, 10, 8, 9, 12, 13, 7, 10, 11, 11, 10, 10, 10, 10, 7, 8, 10, 8, 8, 8, 14, 10, 966094, 8, 10, 9, 12, 6, 12, 11, 4, 8, 9, 8, 11, 119062, 9, 8, 10, 9, 7, 40654, 9, 7, 10, 1774, 6, 10, 5, 7, 7, 8, 8, 7, 6, 6, 12, 11, 7, 9, 12, 9, 11, 6, 8, 11, 6, 7, 9, 10, 10, 12, 14, 10, 10, 8, 8, 5, 7, 9, 13, 10, 9, 10, 12, 6, 6, 10, 9, 5, 12, 11, 11, 9, 10, 13, 13, 7961796, 8, 84638, 13, 13, 6, 8, 9, 7, 5, 10, 15, 11, 13, 10, 11, 9, 11, 11, 6, 11, 12, 10, 12, 10, 7, 8, 7, 10, 11, 7, 9, 8, 11, 7, 11, 11, 9, 5, 1323514, 12, 10, 10, 9, 11, 11, 10, 10, 7, 11, 7, 11, 6, 5, 8, 10, 9, 9, 6, 7, 7, 10, 15, 11, 9, 11, 11, 12, 8, 9, 9, 8, 12, 11, 10, 5, 9, 11, 10, 8, 5, 9, 11, 6, 7, 6, 7, 13, 10, 12, 9, 9, 9, 11, 9, 11, 9, 12, 10, 15, 13, 7, 11, 11, 9, 7, 11, 10, 6, 11, 10, 8, 12, 6, 7, 10, 9, 10556, 10, 11, 14, 9, 10, 8, 9, 7, 9, 6, 12, 12, 12, 13, 7, 9, 1648710, 7, 8, 12, 8, 2336296, 10, 10, 11, 7, 5, 8, 11, 7, 5, 7, 9, 9, 8, 7, 11, 6, 12, 8, 7, 6, 4, 8, 12, 6, 527306525, 12, 15, 6, 5, 10, 5, 11, 13, 11, 8, 5}

Returns: {-1 }
{6, 6, 10, 7, 9, 9, 11, 5, 9, 8, 10, 7, 11, 9, 10, 8, 12, 9, 9, 9, 8, 9, 9, 6, 11, 4, 10, 10, 4, 8, 3, 13, 11, 9, 5, 10, 12, 9, 9, 5, 4, 9, 12, 7, 9, 10, 12, 10, 10, 9, 8, 3963770, 12, 4, 8, 4, 12, 8, 7, 8, 5, 7, 8, 11, 9, 13, 9, 10, 10, 8, 11, 13, 9, 10, 7, 11, 10, 8, 7, 12, 7, 7, 9, 8, 9, 7, 7, 10, 8, 8, 8, 6, 12, 9, 10, 6, 6, 6, 10, 10, 9, 7, 10, 9, 11, 9, 10, 8, 11, 12, 6, 11, 10, 10, 7, 8, 6, 10, 10, 12, 9, 9, 10, 10, 9, 5, 9, 11, 7, 9, 10, 8, 4, 13, 1591, 12, 10, 12, 440581, 10, 10, 12, 9, 10, 6, 8, 8, 9, 9, 8, 5, 6, 10, 9, 2093772, 10, 8, 55980329, 7, 11, 9, 11, 13, 8, 8, 8, 8, 8, 9, 12, 8, 5, 12, 9, 11, 12, 10, 11, 6, 10, 10, 13, 8, 9, 13, 11, 9, 4, 10, 11, 8, 8, 10, 6, 10, 9, 8, 11, 7, 11, 10, 9, 9, 10, 8, 9, 9, 4, 7, 8, 8, 10, 10, 7, 7, 8, 7, 10, 3, 11, 9, 10, 4, 12, 12, 9, 6, 9, 10, 8, 8, 10, 10, 9, 11, 7, 9, 12, 10, 9, 13, 7, 9, 6, 6, 11, 7, 9, 7, 7, 9, 9, 7, 8, 8, 9, 7, 10, 8, 8, 11, 12, 11, 11, 9, 7, 6, 9, 7, 9, 7, 8, 10, 10, 12, 7, 7, 8, 9, 12, 9, 9, 9, 10, 10, 8, 10, 10, 9, 9, 11, 6, 10, 12, 7, 12, 10, 9, 227340910, 14, 8, 9, 11, 10, 8, 11, 9, 8, 10, 5, 13, 9, 8, 10, 9, 9, 7, 10, 11, 12, 12, 10, 9, 8, 6, 9, 9, 5, 9, 7, 12, 9, 10, 12, 12, 12, 12, 6, 12, 8, 69611497, 8, 7, 5, 8, 8, 10, 12, 6, 8, 6, 9, 11, 7, 9, 7, 31228, 10, 11, 9, 9, 13, 7, 5, 7, 10, 10, 10, 7, 31451, 11, 10, 9, 10, 10, 11, 11, 10, 10, 9, 10, 7, 13, 12, 11, 7, 7, 8, 10, 11, 8, 8, 11, 8, 3424, 10, 10, 12, 8, 9, 8, 11, 13, 9, 11, 11, 7, 9, 10, 11, 9, 9, 12, 11, 10, 10, 12, 8, 9, 6, 10, 8, 6, 8, 10, 11, 7, 12, 10, 7, 9, 10, 6, 10, 9, 9, 11, 9, 10, 9, 7, 10, 8, 10, 13, 12, 8, 13, 8, 9, 10, 11, 8, 7, 10, 12, 8, 12, 8, 8, 8, 10, 12, 9, 9, 11, 12, 5, 12, 12, 12, 11, 11, 4, 7, 9, 5, 8, 12, 6, 7, 11, 8, 8, 9, 8, 11, 7, 9, 11, 9, 10, 11, 7, 11, 11, 8, 11, 11, 8, 10, 7, 6, 6, 6, 7, 11, 5, 12, 10, 10, 11, 8, 8, 8, 8, 10, 11, 5, 6, 12, 12, 7, 8, 10, 6, 7, 4, 6, 7, 11, 8, 10, 8, 11, 10, 10, 10, 2, 3, 71336593, 8, 8, 8, 6, 8, 9, 10, 11, 10, 13, 11, 10, 10, 7, 12, 7, 11, 8, 11, 10, 7, 8, 12, 10, 8, 5, 11, 5, 2, 11, 7, 8, 9, 7, 8, 9, 6, 11, 7, 7, 5, 10, 11321, 12, 5, 10, 12, 5, 12, 4, 6, 9, 5, 9, 5, 9, 11, 9, 7, 8, 11, 8, 9, 9, 5, 9, 12, 4, 10, 9, 12, 7, 11, 9803, 9, 8, 261350362, 11, 10, 11, 9, 11, 8, 9, 9, 8, 6, 10046849, 9, 6, 6, 11, 9, 9, 7, 8, 13, 8, 7, 8, 7, 11, 12, 11, 6, 7, 9, 7, 10, 10, 10, 8, 8, 6, 13, 4, 5, 8, 45218, 8, 6, 10, 12, 11, 9, 10, 11, 7, 10, 7, 8, 7, 9, 10, 12, 10, 6, 12, 11, 242803, 3653468, 8, 10, 10, 8, 6, 8, 12, 10, 11, 11, 8, 9, 11, 8, 12, 11, 9, 9, 14, 10, 9, 11, 9, 9, 11, 6, 8, 4, 9, 10, 11, 8, 8, 9, 11, 10, 9, 7, 12, 11, 7, 10, 9, 8, 11, 9, 7, 9, 7, 12, 6, 11, 6, 10, 10, 8, 4, 9, 6, 8, 7, 8, 6, 12, 9, 9, 8, 10, 8, 7, 9, 8, 10, 10, 12, 9, 10, 6, 5, 8, 8, 7, 12, 13, 9, 8, 10, 10878, 9, 5, 6, 9, 11, 12, 11, 10, 11, 8, 10, 13, 9, 8, 12, 7, 7, 8, 8, 11, 9, 9, 6, 7, 8, 10, 11, 9, 9, 11, 9, 10, 2, 5, 6, 6, 6, 8, 8, 10, 11, 9, 12, 8, 9, 11, 9, 8, 7, 9, 10, 11, 10, 9, 12, 7, 11, 10, 9, 10, 5, 7, 12, 9, 10, 9, 8, 7, 5, 10, 500970113, 8, 10, 7, 6, 11, 11, 11, 12, 10, 6, 9, 6, 6, 8, 5, 12, 6, 11, 501115154, 7, 10, 9, 9, 11, 10, 6, 7, 5, 11, 9, 7, 12, 10, 10, 12, 10, 7, 9, 9, 13, 9, 9, 11, 7, 12, 10, 11, 6, 11, 11, 9, 9, 12, 8, 9, 4, 7, 10, 8, 10, 11, 12, 12, 11, 8, 13, 9, 8, 14, 10, 9, 8, 11, 6, 11, 10, 10, 12, 9, 4, 12, 11, 9, 10271906, 9, 9, 11, 6, 9, 9, 10, 11, 9, 7, 4, 6, 10, 10, 8, 6, 6, 6, 10, 5, 9, 10, 10, 8, 8, 11, 7, 10, 11, 8, 17012, 8, 8, 6, 12, 10, 10, 10, 8, 201628, 9, 8, 9, 9, 9, 9, 4, 9, 9, 7, 8, 11, 11, 10, 6, 9, 11, 8, 10, 9, 9, 11, 10, 9, 8, 11, 7, 10, 10, 12, 10, 9}

Returns: {-1 }
{10, 11, 9, 7, 8, 13, 8, 8, 10, 10, 11, 5, 12, 8, 9, 7, 8, 7, 8, 9, 5, 10, 10, 11, 6, 10, 9, 8, 5, 7, 13, 4, 6, 9, 4, 10, 7, 4, 7, 7, 9, 7, 4, 8, 8, 9, 11, 6, 9, 8, 5, 6, 11, 8, 11, 8, 9, 10, 7, 15, 11, 12, 6, 9, 8, 9, 12, 9, 7, 4, 10, 12, 5, 4, 5, 6, 12, 9, 5, 7, 7, 9, 8, 9, 7, 10, 8, 8, 11, 12, 10, 8, 7, 10, 6, 10, 8, 12, 9, 5, 11, 7, 8, 8, 10, 7, 8, 6, 9, 10, 10, 9, 6, 14, 9, 8, 5, 7, 3356, 9, 7, 5, 7, 6, 3, 13, 11, 8, 9, 8, 7, 9, 8, 8, 10, 7, 9, 7, 9, 12, 10, 5, 7, 10, 9, 9, 9, 10, 10, 10, 7, 5, 6, 10, 5, 7, 10, 7, 8, 7, 9, 8, 9, 9, 8, 7, 6, 7, 8, 8, 12, 5, 10, 8, 8, 8, 10, 10, 7, 8, 9, 13, 8, 5, 7, 9, 11, 10, 8, 10, 12, 8, 10, 9, 8, 26522, 7, 5, 10, 8, 11, 9, 9, 10, 7, 9, 10, 8, 11, 9, 11, 7, 10, 7, 6, 9, 4, 7, 9, 9, 7, 13, 7, 6, 11, 6, 10, 7, 10, 6, 8, 7, 11, 8, 11, 9, 7, 8, 5, 10, 8, 7, 7, 12, 9, 11, 10, 6, 11, 9, 11, 7, 8, 9, 6, 10, 8, 12, 4, 8, 8, 11, 6, 7, 5, 13, 10, 10, 11, 8, 7, 8, 8, 7, 11, 12, 5, 10, 11, 4, 9, 5, 10, 9, 7, 4, 5, 8, 7, 10, 14, 10, 10, 6, 8, 7, 6, 8, 10, 9, 9, 15, 9, 9, 9, 10, 11, 7, 4, 8, 9, 8, 8, 10, 10, 9, 10, 9, 6, 10, 11, 11, 5, 6, 6, 4, 10, 10, 9, 7, 5, 6, 6, 8, 9, 6, 9, 9, 13, 10, 7, 4, 8, 10, 10, 10, 7, 12, 8, 11, 10, 6, 9, 11, 8, 10, 7, 9, 13, 10, 9, 8, 12, 10, 9, 8, 7, 6, 3, 7, 7, 7, 7, 7, 11, 7, 11, 11, 13, 7, 6, 8, 8, 10, 10, 8, 8, 10, 10, 9, 9, 6, 9, 9, 7, 8, 9, 8, 4, 9, 8, 11, 9, 8, 9, 9, 6, 11, 7, 12, 7, 8, 10, 8, 7, 4, 8, 8, 10, 10, 11, 6, 11, 8, 7, 4, 8, 8, 7, 5, 8, 11, 10, 9, 5, 10, 8, 8, 7, 6, 8, 9, 9, 10, 11, 8, 7, 5, 9, 8, 8, 14, 8, 8, 6, 7, 12, 8, 8, 8, 4, 5, 8, 10, 10, 10, 9, 8, 10, 11, 7, 6, 9, 10, 8, 13, 7, 7, 5, 7, 9, 6, 9, 11, 8, 10, 6, 9, 7, 10, 9, 8, 8, 9, 5, 9, 8, 5, 8, 11, 4, 10, 13, 9, 9, 6, 8, 9, 9, 11, 6, 7, 9, 6, 7, 10, 9, 11, 11, 7, 10, 7, 11, 9, 6, 9, 8, 11, 10, 9, 9, 10, 8, 8, 7, 8, 8, 8, 8, 9, 10, 8, 9, 7, 9, 10, 6, 13, 7, 11, 10, 12, 10, 10, 8, 5, 8, 11, 6, 9, 7, 8, 9, 9, 9, 11, 8, 9, 8, 8, 8, 6, 10, 5, 13, 11, 8, 9, 7, 9, 9, 10, 12, 7, 6, 11, 7, 9, 11, 10, 7, 8, 7, 10, 14, 4, 10, 4, 12, 2, 10, 6, 10, 9, 9, 7, 7, 11, 11, 4, 8, 9, 11, 5, 8, 9, 7, 8, 9, 6, 6, 9, 8, 10, 9, 13, 9, 10, 8, 11, 8, 6, 9, 4, 8, 10, 10, 10, 9, 12, 8, 6, 10, 10, 9, 6, 15, 9, 10, 7, 6, 9, 5, 6, 10, 13, 12, 8, 7, 8, 9, 9, 7, 7, 10, 11, 10, 10, 11, 3, 7, 8, 10, 9, 9, 8, 9, 9, 9, 10, 6, 10, 6, 8, 9, 9, 8, 9, 10, 9, 10, 7, 10, 8, 8, 8, 9, 9, 9, 8, 10, 3, 10, 6, 8, 11, 9, 5, 9, 10, 7, 10, 8, 7, 9, 6, 4, 11, 8, 11, 7, 9, 6, 12, 10, 6, 8, 11, 7, 10, 8, 8, 8, 6, 9, 6, 9, 4, 10, 5, 9, 5, 6, 8, 11, 8, 8, 7, 4, 9, 9, 11, 7, 5, 8, 9, 5, 6, 8, 8, 8, 12, 11, 9, 7, 10, 7, 7, 10, 11, 7, 9, 8, 12, 8, 11, 12, 13, 8, 9, 11, 8, 13, 10, 8, 6, 7, 10, 13, 9, 12, 10, 12, 8, 11, 7, 10, 7, 7, 9, 7, 10, 10, 7, 8, 10, 9, 10, 9, 8, 7, 6, 9, 8, 9, 10, 11, 10, 12, 6, 7, 7, 9, 11, 10, 8, 8, 10, 10, 8, 6, 6, 6, 11, 9, 9, 9, 8, 11, 11, 10, 9, 9, 8, 12, 7, 8, 7, 9, 4, 8, 11, 9, 8, 8, 12, 7, 7, 8, 11, 6, 8, 10, 8, 7, 10, 8, 13, 12, 10, 7, 5, 5, 11, 9, 10, 4, 10, 8, 11, 9, 8, 5, 9, 8736620, 8, 8, 5, 7, 8, 10, 7, 8, 8, 6, 7, 11, 12, 11, 8, 10, 9, 8, 10, 6, 8, 13, 6, 10, 8, 14, 11, 13, 6, 11, 10, 7, 10, 10, 8, 11, 9, 7, 8, 8, 10, 6, 7, 11, 7, 9, 8, 8, 13, 7, 12, 5, 7, 8, 11, 5, 6, 12, 8, 11, 10, 10, 7, 10, 8, 12, 9, 6, 8, 7, 6, 5, 6, 7, 10, 10, 12, 8, 7, 7, 11, 8, 9, 9, 5}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 5, 11, 14, 10, 15, 15, 9, 11, 7, 12, 7, 9, 9, 9, 7, 10, 7, 6, 4, 9, 8, 10, 4, 9, 12, 6, 14, 10, 8, 10, 11, 5, 13, 12, 8, 13, 9, 11, 15, 9, 13, 12, 10, 15, 8, 7, 11, 10, 5737, 13, 8, 11, 9, 12, 12, 10, 9, 5, 10, 11, 3127, 12, 12, 11, 11, 210343206, 7, 15, 6, 10, 10, 11, 12, 4, 12, 4, 9, 10, 4, 7, 8, 7, 10, 14, 10, 11, 10, 8, 11, 9, 14, 6, 12, 8, 6, 14, 6, 8, 12, 16, 13, 16, 10, 13, 11, 6, 8, 8, 6, 9, 10, 3, 8, 12, 10, 13, 8, 8, 16, 10, 14, 6, 13, 11, 10, 7, 11, 7, 8, 8, 4, 8, 11, 10, 11, 13, 7, 11, 14, 13, 12, 11, 10, 5, 10, 13, 10, 10, 12, 6, 10, 11, 16, 12, 5, 9, 7, 7, 11, 10, 7, 10, 12, 9, 835159, 12, 10, 6, 3, 7, 15, 8, 12, 6, 5, 7, 11, 16, 9, 6, 11, 7, 14, 7, 7, 11, 4, 8, 13, 11, 4, 8, 15, 7, 9, 9, 7, 9, 8, 9, 15, 14, 10, 12, 11, 13, 14, 9, 5, 10, 7, 12, 7, 14, 7, 9, 10, 11, 8, 15, 9, 9, 10, 7, 9, 8, 9, 10, 6, 12, 12, 12, 8, 14, 8, 13, 8, 7, 8, 7, 8, 50879, 14, 8, 10, 7, 12, 14, 8, 11, 15, 11, 4, 9, 7, 11, 10, 9, 8, 12, 10, 11, 11, 10, 8, 15, 13, 4, 7, 11, 9, 7, 8, 10, 10, 11, 8, 11, 9, 8, 13, 7, 12, 13, 11, 11, 11, 9, 10, 11, 11, 12, 12, 10, 8, 6, 10, 13, 7, 10, 9, 3748, 11, 7, 12, 10, 9, 14, 10, 8, 9, 12, 10, 10, 12, 4, 6, 10, 9, 9, 12, 7, 12, 9, 9, 5, 13, 10, 12, 10, 10, 13, 14, 11, 8, 9, 11, 7, 12, 9, 11, 12, 12, 11, 6, 7, 13, 10, 9, 8, 5, 11, 12, 12, 5, 11, 8, 7, 12, 12, 11, 10, 8, 11, 8, 9, 12, 8, 10, 10, 7, 9, 8, 4, 9, 11, 10, 11, 13, 9, 12, 15, 6, 9, 5, 9, 9, 10, 5, 11, 7, 12, 13, 12, 11, 14, 9, 9, 12, 11, 12, 13, 10, 11, 12, 10, 11, 9, 11, 12, 9, 8, 11, 10, 7, 8, 13, 9, 12, 9, 7, 6, 9, 4, 11, 9, 11, 9, 13, 11, 12, 4, 10, 11, 7, 13, 9, 12, 10, 12, 11, 14, 11, 12, 9, 13, 10, 10, 13, 10, 7, 8, 11, 7, 13, 11, 10, 8, 14, 10, 9, 9, 11, 6, 12, 10, 7, 13, 10, 10, 7, 10, 11, 10, 8, 8, 13, 6, 11, 10, 9, 12, 13, 9, 9, 8, 7, 6, 13, 13, 7, 11, 7, 15, 9, 14, 10, 8, 7, 8, 10, 9, 12, 13, 7, 7, 10, 11, 9, 9, 7, 10, 971430, 10, 14, 10, 14770, 9, 8, 3080, 12, 4, 8, 10, 7, 6, 54222, 8, 5, 8, 11, 11, 10, 10, 7, 11, 5, 7, 13, 14, 11, 12, 12, 10, 13, 7, 9, 11, 11, 12, 8, 10, 10, 10, 3, 8, 6, 15, 7, 9, 12, 6, 7, 12, 1496546, 10, 9, 13, 9, 7, 10, 9, 14, 12, 11, 11, 12, 9, 16, 6, 11, 7, 11, 10, 10, 11, 12, 9, 12, 12, 4, 12, 10, 10, 11, 8, 5, 15, 10, 9, 7, 12, 12, 8, 13, 12, 13, 8, 7, 8, 6, 13, 12, 10, 7, 6, 11, 9, 8, 8, 13, 5, 10, 7, 9, 16, 11, 8, 11, 13, 14, 8, 6, 24539350, 11, 8, 12, 10, 11, 8, 6, 13, 11, 4, 7, 12, 12, 8, 11, 11, 11, 8, 8, 7, 12, 11, 10, 11, 9, 6, 11, 7, 15, 10, 5, 10, 6, 6, 9, 9, 12, 7, 9, 10, 11, 7, 9, 11, 8, 11, 10, 7, 5, 10, 9, 7, 7, 4, 7, 10, 10, 14, 8, 12, 9, 7, 11, 8, 7, 5, 10, 10, 11, 11, 11, 8, 10, 3, 13, 7, 14, 11, 6, 8, 11, 10, 9, 14, 8, 10, 9, 5, 12, 10, 11, 8689418, 10, 10, 13, 4, 13, 8, 10, 8, 8, 9, 14, 8, 9, 13, 13, 15, 7, 7, 14, 13, 11, 8, 9, 8, 10, 5, 8, 10, 5, 10, 12, 13, 13, 10, 10, 11, 10, 14, 14, 9, 9, 11, 7, 7, 13, 8, 16, 14, 8, 5, 7, 10, 11, 12, 9, 10, 7, 9, 12, 7, 8, 11, 11, 3, 7, 11, 11, 6, 4, 11, 5, 11, 8, 12, 11, 7, 10, 11, 12, 10, 3, 7, 5, 8, 7, 7, 7, 10, 11, 7, 13, 10, 7, 9, 13, 13, 12, 6, 9, 12, 7, 7, 10, 11, 13, 12, 14, 10, 13, 12, 6, 9, 7, 11, 7, 7, 13, 10, 12, 13, 10, 11, 8, 9, 8, 9, 8, 10, 10, 9, 13, 8, 9, 6, 10, 10, 208650939, 12, 10, 10, 3, 7, 9, 8, 9, 11, 7, 9, 13, 9, 9, 5, 12, 9, 14, 7, 11, 8, 11, 10, 9, 8, 3, 15, 10, 13, 12, 8, 13, 12, 2, 10, 11, 9, 13, 9, 11, 8, 10, 11, 10, 12, 11, 10, 14, 13, 7, 10, 5, 10, 9, 9, 12, 11, 14, 10, 9, 13, 14, 11, 10, 9, 3, 11, 12, 11, 14, 16, 8, 8, 9, 13, 7, 10, 12, 9, 7, 7, 7, 11, 11, 13, 7, 4, 13, 11, 13, 9, 12, 3, 6, 9, 12, 10, 11, 12, 12, 10, 10, 6, 7, 13, 13, 13, 9, 7, 8, 12, 8, 9, 8, 12, 11, 4, 10, 6, 5, 11}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{7, 7, 11, 8, 2, 12, 7, 14, 9, 7, 5, 11, 7, 10, 10, 8, 8, 4, 13, 9, 12, 4, 8, 7, 7, 13, 7, 10, 12, 6, 9, 8, 10, 6, 9, 7, 6, 8, 10, 8, 6, 10, 7, 9, 8, 9, 5, 11, 11, 6, 12, 9, 11, 6, 9, 12, 14, 11, 13, 8, 10, 9, 16, 6, 5, 10, 11, 5, 5, 8, 8, 10, 11, 10, 5, 7, 7, 8, 11, 11, 9, 9, 12, 12, 10, 9, 4, 9, 6, 9, 12, 6, 10, 12, 10, 8, 10, 6, 10, 5, 10, 13, 8, 8, 10, 8, 15, 9, 10, 7, 10, 8, 10, 6, 6, 6, 11, 6, 8, 4, 11, 8, 9, 10, 9, 10, 8, 13, 9, 10, 10, 7, 15, 4, 11, 12, 4, 12, 10, 7, 11, 10, 7, 9, 8, 9, 9, 13, 7, 6, 8, 9, 8, 7, 11, 10, 5, 8, 12, 14, 9, 10, 7, 6, 12, 13, 8, 7, 6, 7, 10, 14, 8, 12, 8, 6, 8, 12, 5, 10, 8, 9, 9, 8, 8, 11, 13, 10, 10, 5, 7, 12, 10, 9, 11, 7, 10, 9, 8, 6, 10, 6, 11, 6, 9, 6, 12, 9, 7, 8, 9, 5, 6, 7, 8, 10, 12, 8, 11, 11, 8, 6, 12, 5, 8, 9, 7, 9, 8, 7, 11, 14, 11, 5054, 9, 4, 5, 9, 14, 8, 11, 14, 11, 6, 8, 12, 9, 10, 12, 9, 10, 6, 14, 8, 6, 8, 11, 12, 9, 6, 5, 9, 12, 7, 7, 10, 11, 12, 7, 10, 15, 6, 10, 11, 12, 11, 8, 8, 8, 7, 9, 8, 9, 11, 11, 8, 10, 11, 12, 4, 8, 9, 9, 9, 10, 13, 7, 9, 13, 12, 10, 11, 10, 10, 12, 9, 9, 13, 5, 6, 5, 13, 9, 8, 9, 13, 10, 8, 9, 10, 9, 7, 9, 11, 12, 9, 10, 11, 13, 11, 9, 7, 7, 10, 8, 13, 5, 5, 9, 9, 4, 8, 13, 6, 5, 5, 12, 9, 7, 9, 6, 7, 8, 6, 5, 13, 12, 9, 11, 9, 9, 10, 9, 7, 10, 10, 6, 12, 12, 16, 11, 7, 11, 7, 11, 9, 10, 11, 7, 9, 16, 11, 5, 6, 8, 14, 10, 11, 9, 10, 9, 12, 10, 8, 7, 5, 15, 8, 7, 11, 9, 12, 7, 10, 8, 9, 6, 10, 10, 14, 8, 8, 7, 5, 5, 9, 13, 12, 8, 8, 7, 10, 11, 8, 7, 10, 12, 6, 11, 7, 11, 5, 7, 12, 5, 5, 9, 12, 6, 9, 11, 7, 10, 5, 11, 9, 10, 8, 8, 9, 3, 6, 10, 6, 10, 12, 8, 7, 9, 8, 9, 11, 6, 10, 9, 9, 10, 8, 10, 7, 10, 14, 9, 8, 9, 11, 6, 9, 11, 6, 7, 6, 10, 6, 7, 11, 11, 8, 6, 7, 9, 11, 8, 10, 10, 8, 13, 10, 6, 5, 10, 8, 9, 3, 10, 10, 8, 6, 12, 6, 6, 9, 12, 7, 9, 7, 10, 6, 8, 6, 4, 9, 8, 8, 7, 8, 9, 6, 9, 10, 8, 11, 12, 3, 8, 15, 12, 9, 10, 9, 9, 8, 6, 11, 5, 9, 9, 7, 5, 9, 10, 8, 10, 13, 7, 10, 8, 8, 8, 7, 5, 10, 12, 6, 11, 10, 10, 7, 13, 9, 13, 4, 12, 13, 6, 12, 11, 12, 13, 5, 8, 10, 7, 10, 9, 9, 11, 10, 7, 8, 12, 7, 10, 4, 11, 7, 8, 12, 5, 10, 11, 11, 9, 6, 11, 12, 11, 13, 10, 6, 13, 6, 10, 4, 8, 8, 7, 5, 8, 11, 10, 9, 10, 8, 10, 12, 6, 10, 85088899, 6, 7, 12, 8, 11, 7, 8, 6, 11, 9, 11, 9, 12, 8, 11, 3, 11, 8, 9, 6, 11, 11, 7, 7, 11, 11, 10, 5, 8, 9, 12, 9, 7, 4, 4, 7, 8, 12, 6, 12, 9, 8, 8, 7, 6, 12, 8, 7, 8, 9, 10, 8, 10, 11, 9, 11, 10, 6, 10, 7, 12, 12, 12, 12, 4, 9, 6, 8, 14, 9, 8, 10, 9, 10, 9, 11, 11, 6, 12, 10, 9, 9, 10, 6, 9, 10, 12, 13, 8, 7, 5, 8, 12, 13, 5, 9, 16, 5, 4, 13, 5, 10, 10, 12, 6, 4, 13, 8, 8, 8, 11, 10, 9, 9, 6, 9, 10, 6, 7, 9, 10, 10, 9, 10, 9, 4, 5, 15, 16, 9, 5, 10, 9, 8, 12, 10, 5, 10, 9, 10, 12, 9, 11, 5, 6, 8, 6, 5, 11, 16, 12, 11, 5, 4, 9, 11, 8, 7, 5, 13, 4, 11, 5, 11, 8, 9, 7, 13, 7, 12, 7, 7, 7, 9, 8, 7, 10, 8, 9, 6, 12, 6, 8, 12, 9, 10, 11, 9, 8, 12, 9, 7, 9, 6, 13, 9, 7, 13, 5, 9, 8, 11, 10, 5, 13, 6, 14, 11, 12, 12, 9, 10, 8, 5, 6, 9, 7, 8, 9, 9, 9, 5, 9, 7, 12, 7, 6, 6, 12, 10, 11, 11, 6, 11, 5, 12, 8, 7, 6, 4, 10, 12, 7, 10, 5, 11, 9, 8, 12, 8, 6, 8, 9, 7, 7, 7, 11, 8, 7, 8, 6, 11, 5, 12, 10, 9, 11, 6, 10, 11, 10, 10, 7, 9, 9, 8, 9, 12, 7, 14, 5, 9, 9, 8, 12108855, 12, 11, 5, 6, 12, 7, 10, 11, 9, 10, 9, 10, 5, 12, 10, 9, 8, 6, 12, 11, 15, 10, 10, 13, 7, 8, 7, 9, 8, 10, 12, 6, 10, 7, 11, 8, 8, 12, 14, 8, 4, 10, 9, 11, 11, 9, 11, 11, 4, 8, 12, 12, 12, 9, 11, 11, 10, 6}

Returns: {2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{5, 10, 6, 14, 12, 11, 12, 12, 10, 10, 9, 6, 11, 11, 7, 11, 7, 8, 5, 13, 12, 8, 13, 8, 11, 12, 10, 10, 10, 12, 15, 9, 8, 11, 15, 10, 13, 14, 11, 8, 15, 9, 11, 8, 9, 11, 13, 14, 10, 12, 9, 10, 15, 8, 8, 11, 13, 4, 6, 10, 9, 6, 7, 8, 13, 13, 7, 9, 13, 8, 12, 9, 9, 5, 8, 7, 10, 9, 11, 10, 12, 9, 3, 11, 7, 12, 10, 9, 4, 10, 14, 12, 11, 15, 10, 12, 10, 4, 9, 5, 9, 6, 12, 9, 10, 13, 11, 12, 10, 12, 10, 6, 11, 5, 8, 11, 8, 10, 14, 13, 3, 9, 10, 6, 13, 9, 13, 7, 10, 8, 9, 12, 5, 4, 11, 10, 11, 9, 11, 11, 11, 12, 8, 11, 10, 13, 6, 9, 9, 11, 10, 13, 11, 8, 7, 15, 13, 9, 11, 9, 6, 4, 7, 9, 14, 4, 10, 9, 10, 7, 14, 7, 7, 12, 14, 11, 8, 11, 12, 10, 9, 13, 7, 11, 9, 13, 11, 7, 12, 9, 10, 12, 25091440, 12, 7, 12, 5, 10, 7, 10, 11, 11, 9, 8, 9, 10, 10, 11, 14, 11, 3, 12, 11, 13, 12, 10, 12, 11, 3, 11, 14, 7, 8, 11, 9, 6, 13, 12, 11, 9, 14, 9, 7, 11, 10, 11, 7, 4, 11, 10, 10, 12, 10, 13, 10, 9, 7, 10, 2200851, 10, 12, 3, 12, 8, 9, 5, 9, 9, 11, 10, 12, 10, 11, 10, 12, 11, 11, 10, 9, 11, 11, 14, 7, 10, 10, 13, 10, 9, 9, 9, 13, 7, 11, 7, 7, 11, 8, 6, 3548174, 9, 10, 10, 9, 7, 10, 13, 6, 8, 7, 9, 13, 4, 12, 13, 7, 8, 7, 12, 15, 11, 7887, 8, 13, 10, 5, 11, 12, 13, 10, 6, 9, 7, 15, 10, 10, 10, 6, 12, 12, 6, 12, 11, 8, 9, 10, 9, 8, 11, 8, 14, 11, 10, 15, 10, 9, 6, 10, 10, 10, 10, 10, 7, 8, 9, 9, 9, 4, 7, 12, 8, 10, 7, 13, 6, 12, 12, 7, 10, 10, 8, 6, 10, 11, 8, 5, 6, 6, 13, 11, 9, 10, 12, 10, 12, 9, 12, 8, 13, 11, 11, 12, 8, 8, 10, 9, 12, 14, 10, 12, 12, 13, 9, 7, 12, 9, 11, 12, 14, 11, 9, 6, 8, 14, 9, 11, 12, 10, 9, 14, 11, 9, 8, 9, 5, 9, 4, 14, 13, 5, 220530, 11, 9, 10, 4, 11, 8, 8, 9, 10, 11, 11, 8, 6, 9, 8, 10, 13, 8, 9, 10, 10, 14, 11, 12, 12, 9, 9, 10, 13, 11, 12, 11, 7, 10, 14, 6, 14, 10, 10, 6, 12, 9, 8, 11, 2071, 9, 5, 7, 12, 14, 13, 9, 11, 10, 13, 5, 10, 10, 10, 6, 11, 10, 10, 12, 14, 12, 13, 8, 11, 2987398, 10, 10, 9, 6, 3, 12, 12, 10, 10, 14, 10, 2, 10, 7, 11, 12, 11, 12, 13, 11, 9, 5, 7, 4, 8, 9, 11, 8, 10, 10, 9, 11, 10, 8, 13, 12, 4, 5, 11, 7, 10, 12, 12, 9, 9, 9, 9, 9, 10, 1923948, 11, 11, 10, 11, 11, 12, 10, 9, 4, 12, 12, 11, 14, 11, 13, 13, 5, 6, 9, 10, 8, 10, 9, 10, 11, 3, 10, 9, 9, 8, 5, 12, 12, 11, 14, 12, 7, 10, 10, 11, 10, 7, 11, 6, 7, 9, 14, 14, 12, 14, 10, 13, 10, 8, 10, 14, 8, 12, 8, 12, 5, 7, 10, 12, 9, 12, 11, 8, 7, 9, 13, 10, 9, 10, 6, 13, 5, 7, 12, 8, 11, 10, 10, 10, 6, 9, 12, 7, 312822, 11, 5, 10, 7, 7, 10, 11, 13, 10, 11, 9, 12, 5, 13, 10, 10, 9, 9, 9, 10, 9, 10, 9, 8, 7, 11, 9, 11, 10, 9, 10, 13, 9, 12, 15, 10, 9, 10, 11, 14, 11, 11, 5, 10, 10, 9, 11, 11, 10, 9, 13, 10, 6, 9, 13, 10, 12, 11, 13, 10, 8, 9, 13, 12, 8, 10, 9, 8, 6, 7, 8, 12, 7, 10, 11, 7, 8, 12, 9, 14, 7, 6, 9, 11, 12, 8, 10, 10, 11, 7, 13, 12, 8, 11, 9, 7, 4, 7, 11, 10, 11, 7, 13, 10, 404526, 7, 5, 1693119, 13, 12, 8, 10, 11, 13, 10, 14, 9, 15, 7, 9, 12, 9, 10, 10, 11, 8, 8, 8, 9, 12, 6, 8, 12, 14, 13, 10, 5, 25171721, 2, 12, 5, 9, 11, 9, 12, 11, 9, 49854939, 10, 6, 7, 8, 10, 10, 9, 10, 10, 11, 4, 10, 9, 10, 9, 12, 8, 10, 9, 10, 6, 10, 6, 12, 8, 12, 7, 7, 12, 12, 12, 13, 6, 9, 10, 9, 13, 12, 10, 12, 10, 9, 5, 12, 10, 10, 6, 10, 8, 13, 11, 9, 10, 5, 13, 13, 8, 12, 11, 9, 15, 8, 11, 8, 11, 10, 4, 14, 7, 8, 11, 10, 12, 11, 6, 10, 6, 9, 10, 7, 12, 12, 13, 10, 8, 9, 7, 12, 7, 10, 10, 10, 13, 9, 10, 9, 8, 13, 10, 10, 15, 13, 8, 13, 10, 12, 11, 9, 10, 10, 10, 9, 11, 12, 13, 10, 6, 11, 9, 13, 9, 11, 12, 11, 10, 9, 12, 15, 5, 7, 12, 11, 7, 9, 8, 9, 12, 13, 10, 6, 6, 7, 11, 10, 13, 7, 6, 9, 12, 3, 12, 6, 14, 9, 10, 10, 9, 61156622, 6, 9, 9, 12, 11, 8, 13, 11, 6, 11, 8, 9, 9, 11, 8, 14, 12, 7, 8, 10, 5, 9, 10, 10, 6, 15, 10, 10, 8, 12, 8, 6, 12, 10, 6, 13, 11, 9, 11, 5, 4, 11, 10, 5, 10, 8, 8, 210255708, 7, 11, 13}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{9, 466338, 11, 7, 10, 11, 5, 11, 8, 7, 11, 10, 7, 8, 8, 6, 12, 9, 16, 9, 4070, 10, 12, 7, 11, 11, 8, 10, 11, 13, 13, 10, 10, 5, 8, 8, 9, 5, 8, 5, 5, 8, 5, 8, 8, 9, 12, 9, 9, 10, 6, 7, 11, 7, 7, 8, 8, 12, 9, 7, 61206, 7, 9, 10, 8, 8, 8, 8, 13, 9, 5, 8, 12, 9, 10, 5, 11, 6, 10, 7, 9, 12, 4, 9, 10, 10, 5, 12, 11, 5, 6, 8, 9, 10, 6, 12, 13, 5, 6, 5, 6, 11, 9, 10, 5, 3, 5, 7, 8, 7, 10, 7, 7, 12, 13, 9, 7, 10, 9, 6, 6, 8, 16, 11, 6, 4, 7, 8, 8, 8, 8, 7, 12, 11, 8, 11, 10, 11, 10, 8, 9, 9, 8, 11, 7, 8, 9, 9, 10, 9, 12, 8, 10, 10, 5, 10, 13, 9, 8, 12, 5, 11, 6, 7, 11, 7, 8, 13, 7, 951297, 6, 11, 9, 8, 8, 10, 14, 6, 10, 12, 11, 8, 11, 8, 10, 8, 8, 13, 8, 6, 9, 7, 8, 9, 7, 6, 10, 6, 10, 10, 8, 7, 7, 6, 10, 9, 12, 12, 7, 7, 9, 10, 10, 11, 9, 6, 38036, 6, 8, 28020878, 8, 9, 7, 10, 11, 3, 10, 7, 9, 4, 6, 9, 7, 7, 11, 9, 8, 7, 8, 5, 5, 11, 5, 10, 10, 9, 8, 10, 9, 7, 5, 8, 4, 8, 9, 10, 8, 9, 10, 11, 5, 10, 6, 7, 11, 7, 8, 9, 11, 9, 10, 6, 9, 9, 9, 11, 8, 9, 8, 5, 9, 10, 6, 6, 7, 5, 11, 10, 7, 9, 9, 12, 5, 10, 5, 12, 8, 9, 11, 9, 11, 9, 11, 13, 10, 1106079, 11, 6, 9, 8, 9, 8, 11, 10, 10, 4, 7, 10, 8, 7, 10, 11, 8, 8, 7, 8, 6, 8, 9, 8, 10, 9, 13, 7, 8, 10, 8, 7, 9, 9, 9, 13, 297094, 8, 12, 8, 6, 24900508, 9, 5, 11, 9, 21896, 14, 9, 9, 8, 8, 7, 8, 12, 6, 9, 11, 7, 7, 7, 11, 7, 9, 8, 10, 9, 9, 7, 7, 6, 11, 9, 8, 11, 12, 8, 6, 15, 8, 12, 8, 11, 8, 11, 9, 11, 10, 11, 10, 12, 6, 7, 6, 8, 9, 12, 9, 8, 5, 11, 5, 5, 10, 11, 12, 9, 8, 9, 14, 6, 4, 8, 10, 5, 9, 8, 5, 9, 9, 6, 6, 10, 7, 6, 5, 6, 9, 5, 10, 7, 6, 7, 7, 10, 9, 10, 8, 13, 8, 7, 12, 7, 242070117, 9, 7, 11, 7, 10, 6, 11, 6, 11, 13, 10, 13, 11, 8, 9, 10, 69024, 8, 9, 8, 9, 8, 10, 10, 7, 12, 11, 9, 7, 6, 11, 9, 7, 4, 13, 7, 10, 10, 8, 1920, 8, 5, 10, 10, 10, 11, 11, 16, 4, 7, 2912, 10, 8, 8, 8, 7, 15, 11, 6738, 8, 4, 7, 8, 8, 8, 11, 8, 13, 6, 10, 10, 7, 8, 13, 6, 5, 11, 2, 7, 13, 8, 10, 13, 8, 6, 9, 9, 6, 8, 12, 11, 11, 10, 8, 9, 8, 13, 9, 35948389, 12, 11, 4, 8, 8, 7, 11, 9, 8, 10, 11, 6, 8, 11, 9, 8, 11, 8, 8, 5, 6, 10, 7, 9, 8, 11, 9, 11, 8, 14, 7, 5, 13, 8, 9, 11, 11, 8, 8, 12, 8, 10, 8, 14, 8, 7, 9, 6, 10, 10, 9, 12, 9, 10, 7, 9, 7, 8, 9, 7, 11, 11, 6, 10, 6, 11, 10, 9, 9, 10, 10, 9, 5, 9, 8, 10, 9, 8, 8, 13, 8, 8, 7, 11, 10, 8, 9, 8, 6, 8, 8, 7, 6, 7, 8, 13, 7, 7, 10, 9, 8, 9, 4, 8, 12, 9, 11, 10, 7, 7, 6, 13, 8, 10, 6, 5, 12, 9, 11, 10, 8, 7, 9, 12, 7, 7, 10, 6, 9, 5, 8, 6, 13, 7, 7, 8, 8, 7, 8, 10, 6, 6, 10, 8, 9, 7, 8, 10, 7, 11, 9, 7, 10, 6, 7, 11, 5, 12, 9, 9, 5, 5, 8, 7, 9, 8, 12, 12, 8, 14, 10, 11, 7, 6, 9, 4, 9, 9, 11, 6, 8, 7, 10, 12, 8, 12, 5, 8, 8, 9, 8, 7, 7, 9, 10, 9, 12, 6, 6, 7, 10, 12, 12, 10, 9, 10, 9, 6, 6, 6, 6, 6, 8, 6, 2, 8, 10, 12, 6, 8, 10, 7, 11, 10, 10, 8, 11, 5, 6, 12, 8, 9, 11, 6, 9, 9, 11, 6, 7, 8, 11, 5, 8, 10, 8, 9, 11, 9, 8, 11, 12, 9, 7, 11, 11, 7, 11, 7, 13, 6, 12, 8, 3, 9, 8, 12, 6, 13, 12, 9, 9, 7, 11, 10, 8, 11, 12, 11, 7, 12, 7, 10, 9, 9, 11, 13, 11, 9, 22932377, 10, 11, 9, 9, 6, 6, 9, 8, 347222, 7, 11, 11, 15, 9, 8, 7, 12, 8, 8, 9, 5, 10, 10, 12, 8, 7, 9, 6, 13, 6, 6, 8, 10, 8, 9, 11, 5, 12, 5, 6, 10, 10, 13, 12, 8, 13, 11, 3, 13, 11, 12, 11, 9, 9, 14, 11, 11, 7, 9, 5, 10, 9, 7, 7, 10, 8, 10, 11, 9, 9, 10, 15, 11, 4, 9, 11, 5, 14, 49081, 9, 9, 8, 9, 9, 8, 9, 12, 5, 14, 12, 6, 6, 6, 8, 11, 13, 15, 7, 6, 10, 7, 8, 9, 6, 10, 5, 13, 10, 8, 8, 13, 10, 9, 13, 7, 8, 13, 7, 8, 8, 11, 10, 8, 7, 7, 11, 7, 12, 9, 9, 6, 9, 4, 6, 6, 4, 14, 9, 8, 6, 10, 10, 10, 6, 6, 7, 6, 10, 9, 13, 8, 12, 5, 11, 11, 10, 11, 11, 7, 12, 7, 6}

Returns: {-1 }
{19, 3213641, 17, 8, 15, 13, 14, 14, 14, 6, 9, 13, 12, 13, 13, 13, 10, 13, 10, 15, 9, 12, 19, 15, 12, 3, 47218445, 15, 14, 12, 12, 15, 12, 9, 6, 9, 15, 11, 17, 13, 17, 15, 10, 12, 10, 7, 10, 6, 6, 16, 7, 15, 13, 13, 16, 6, 12, 17, 19, 14, 17, 16, 6, 16, 14, 10, 51452894, 8, 16, 11, 9, 11, 14, 12, 7, 19, 11, 15, 7, 16, 8, 6, 7, 3, 13, 11, 12, 10, 981680, 15, 7, 11, 14, 12, 12, 18, 8, 9, 14, 10, 12, 11, 6, 14, 17, 12, 6, 3, 14, 15, 13, 18, 17, 13, 8, 14, 8, 16, 16, 13, 17, 11, 12, 7, 11, 8, 13, 14, 16, 8, 15, 15, 15, 8, 11, 13, 6, 13, 17, 17, 8, 12, 12, 7, 7, 13, 14, 6, 12, 12, 6, 11, 11, 16, 6, 6, 7, 14, 11, 12, 12, 15, 9, 9, 16, 9, 18, 12, 13, 3, 17, 14, 7, 10, 8, 7, 11, 12, 18, 6, 15, 9, 13, 3, 17, 10, 14, 12, 14, 12, 13, 6, 14, 8, 10, 12, 10, 14, 9, 13, 14, 6, 15, 14, 15, 6, 12, 12, 5, 12, 13, 6, 9, 9, 17, 12, 10, 14, 8, 12, 17, 14, 14, 16, 12, 12, 10, 9, 13, 17, 14, 14, 6, 14, 12, 13, 12, 13, 3, 9, 14, 13, 14, 14, 11, 11, 18, 13, 8, 13, 16, 12, 14, 11, 12, 12, 9, 7, 14, 6, 9, 15, 6, 13, 16, 9, 12, 6, 8, 14, 13, 6, 19, 8, 11, 9, 19, 19, 9, 15, 10, 18, 11, 10, 15, 15, 15, 19, 11, 17, 12, 19, 14, 12, 10, 12, 11, 14, 10, 12, 12, 4, 2, 7, 13, 7, 13, 8, 16, 14, 7, 12, 6, 7, 14, 11, 5, 7, 11, 14, 12, 17, 15, 8, 13, 15, 13, 11, 14, 13, 10, 13, 11, 10, 14, 15, 13, 15, 18, 7, 3, 13, 9, 15, 12, 11, 13, 12, 12, 11, 17, 12, 3, 12, 6, 12, 10, 10, 9688264, 9, 7, 8, 17, 5, 11, 14, 13, 12, 12, 14, 13, 13, 9, 7, 12, 13, 16, 12, 16, 7, 9, 14, 10, 7, 282697, 9, 15, 6, 10, 13, 8, 6, 11, 12, 17, 15, 12, 10, 13, 7, 6, 13, 13, 12, 10, 14, 9, 13, 10, 5, 8, 4, 3696446, 6, 17, 8, 18, 11, 10, 13, 15, 14, 15, 14, 9, 5, 5, 12, 11, 16, 6, 12, 14, 8, 12, 10, 10, 14, 13, 13, 12, 12, 17, 16, 14, 10, 4, 10, 7, 16, 11, 12, 14, 15, 10, 14, 12, 13, 14, 7, 13, 5901, 6, 10, 9, 12, 12, 13, 18, 8, 12, 9, 11, 14, 10, 8, 11, 13, 10, 14, 15, 15, 12, 11, 6, 14, 8, 11, 15, 7, 15, 13, 16, 19, 5, 11, 15, 11, 7, 12, 12, 8, 14, 12, 15, 16, 12, 11, 8, 10, 5, 7, 15, 5, 11, 16, 6, 12, 9, 15, 15, 8, 12, 15, 13, 16, 17, 9, 6, 5, 11, 14, 17, 12, 7, 13, 12, 7, 9, 5, 6, 14, 4, 11, 12, 11, 12, 12, 9, 13, 15, 12, 16, 7, 15, 10, 10, 12, 12, 9, 13, 7, 17, 15, 17, 14, 14, 6, 13, 11, 13, 12, 10, 8, 10, 5, 14, 11, 16, 10, 14, 12, 9, 14, 10, 4, 14, 8, 9, 16, 14, 7, 9, 19, 13, 6, 7, 9, 11, 16, 8, 11, 7, 9, 14, 9, 5, 5, 16512336, 15, 7, 15, 13, 9, 8, 17, 16, 11, 15, 8, 7, 10, 11, 13, 14, 7, 17, 14, 9, 16, 15, 5, 11, 8, 10, 11, 5, 362108, 9, 12, 19, 6, 7, 6, 6, 7, 14, 15, 5, 13, 15, 12, 15, 13, 14, 4, 14, 14, 13, 15, 16, 12, 10, 10, 9, 17, 7, 9, 13, 13, 17, 3, 6, 4, 15, 19, 9, 9, 11, 10, 15, 17, 11, 13, 11, 8, 14, 16, 14, 8, 12, 14, 6, 9, 7, 5, 12, 13, 7, 12, 15, 14, 9, 13, 15, 2, 11, 4, 14, 12, 9, 14, 5, 6, 15, 14, 11, 17, 16, 9, 16, 13, 8, 12, 19, 14, 15, 15, 9, 15, 10, 13, 9, 16, 6, 15, 15, 7, 7, 10, 15, 14, 8, 10, 13, 10, 12, 13, 12, 9, 8, 15, 12, 6, 8, 11, 7, 8, 12, 12, 15, 14, 14, 14, 11, 12, 11, 13, 6, 10, 12, 6, 13, 8, 7, 4, 13, 16, 7, 12, 11, 6, 9, 7, 14, 9, 7, 8, 14, 10, 15, 11, 13, 9, 10, 17, 13, 10, 10, 14, 13, 14, 12, 6, 15, 8, 4, 12, 9, 7, 8, 10, 13, 4, 11, 9, 12, 8, 15, 12, 10, 13, 12, 13, 7, 13, 15, 13, 14, 6, 13, 12, 13, 8, 7, 7, 14, 8, 6, 11, 12, 16, 3, 13, 11, 13, 9, 12, 4, 11, 7, 13, 9, 6, 8, 15, 18, 11, 12, 4, 14, 11, 4, 4, 15, 16, 8, 14, 12, 17, 8, 12, 7, 8, 12, 11, 11, 6, 14, 15, 12, 13, 12, 11, 6, 13, 10, 8, 7, 13, 6, 15, 18, 16, 18, 10, 6, 8, 12, 10, 16, 11, 12, 14, 15, 14, 15, 13, 14, 12, 6, 10, 15, 10, 6, 12, 8, 14, 14, 8, 8, 19, 11, 11, 16, 13, 10, 6, 14, 13, 10, 13, 6, 9, 11, 15, 14, 15, 15, 9, 14, 17, 10, 10, 17, 13, 8, 13, 8, 15, 13, 16, 10, 14, 15, 8, 17, 13, 11, 10, 4, 7, 5, 9, 11, 17, 13, 10, 15, 8, 1068972, 14, 13, 17, 12, 9, 7, 18, 12, 11, 8, 16, 10, 10, 10, 7, 7, 10, 16, 13, 15, 14, 8, 16, 7, 14}

Returns: {-1 }
{8, 11, 10, 7, 9, 11, 8, 14, 11, 3, 5, 16, 10, 11, 9, 11, 8, 7, 15, 10, 12, 8, 9, 12, 13, 13, 12, 9, 9, 6, 12, 13, 14, 12, 9, 12, 10, 15, 9, 11, 9, 5, 6, 7, 13, 5, 12, 14, 9, 4, 9, 11, 14, 3, 7, 9, 5, 14, 7, 8, 14, 14, 13, 12, 11, 13, 12, 7, 11, 11, 14, 12, 6, 15, 11, 14, 16, 13, 11, 10, 13, 12, 9, 11, 5, 12, 7, 14, 9, 8, 12, 5, 7, 8, 9, 8, 9, 12, 9, 15, 9, 13, 10, 10, 8, 11, 7, 16, 7, 12, 12, 14, 13, 10, 9, 11, 11, 10, 9, 11, 12, 9, 14, 13, 11, 8, 5, 9, 12, 5, 15, 9, 13, 8, 6, 14, 11, 9, 9, 11, 8, 13, 6, 3, 13, 11, 13, 14, 15, 12, 15, 14, 10, 12, 11, 6, 8, 14, 9, 8, 8, 4, 12, 10, 11, 12, 12, 9, 9, 12, 12, 12, 11, 8, 13, 10, 8, 8, 8, 13, 4, 6, 7, 13, 5, 8, 8, 8, 9, 12, 6, 11, 9, 15, 10, 7, 8, 15, 15, 5, 9, 9, 4, 9, 12, 6, 10, 7, 13, 7, 5, 11, 11, 10, 10, 12, 7, 15, 8, 14, 8, 14, 10, 10, 9, 13, 8, 12, 11, 12, 12, 12, 7, 14, 14, 12, 12, 16, 11, 11, 9, 11, 15, 11, 11, 5, 10, 16, 13, 14, 15, 15, 9, 7, 14, 8, 11, 14, 11, 15, 12, 12, 13, 12, 8, 10, 12, 7, 13, 11, 8, 11, 7, 8, 12, 14, 12, 8, 9, 9, 5, 6, 11, 14, 15, 9, 15, 14, 13, 13, 15, 6, 9, 11, 14, 16, 6, 7, 13, 9, 12, 14, 11, 4, 14, 12, 10, 6, 13, 11, 11, 11, 12, 13, 11, 12, 15, 10, 12, 12, 14, 14, 10, 12, 27991, 13, 7, 8, 8, 15, 5, 14, 11, 8, 10, 9, 10, 12, 9, 8, 11, 7, 10, 17, 11, 12, 5, 15, 8, 10, 9, 11, 10, 6, 12, 9, 4, 15, 15, 10, 13, 13, 8, 15, 13, 10, 7, 13, 11, 12, 11, 13, 13, 6, 10, 14, 12, 10, 13, 14, 5, 6, 12, 8, 15, 13, 12, 4, 10, 10, 13, 8, 9, 3, 14, 14, 7, 11, 17, 9, 13, 7, 9, 7, 4, 15, 8, 12, 8, 14, 10, 11, 9, 9, 10, 6, 11, 8, 15, 11, 12, 11, 15, 10, 10, 10, 14, 10, 13, 7, 8, 10, 12, 11, 10, 7, 4, 9, 4, 9, 10, 13, 9, 12, 5, 16, 10, 12, 13, 14, 13, 6, 7, 10, 7, 7, 12, 3, 14, 6, 13, 11, 12, 11, 11, 8, 5, 6, 8, 14, 9, 4, 12, 7, 8, 5, 11, 11, 15, 10, 6, 14, 8, 13, 15, 7, 10, 9, 12, 8, 10, 8, 8, 10, 15, 10, 11, 11, 10, 12, 10, 4, 13, 13, 10, 12, 11, 9, 8, 7, 10, 10, 3, 7, 8, 12, 10, 10, 11, 11, 6, 14, 14, 12, 11, 13, 12, 8, 9, 10, 6, 14, 6, 9, 13, 15, 13, 8, 13, 11, 12, 14, 15, 11, 11, 10, 13, 15, 9, 11, 15, 9, 11, 12, 6, 13, 8, 7, 11, 8, 9, 8, 14, 11, 14, 9, 9, 7, 10, 9, 18, 12, 5, 14, 8, 8, 10, 9, 9, 4, 13, 16, 5, 9, 13, 5, 10, 14, 11, 12, 11, 9, 14, 10, 8, 16, 10, 11, 10, 6, 9, 10, 4, 11, 10, 9, 11, 8, 10, 10, 6, 1194298, 8, 13, 12, 11, 7, 12, 14, 12, 8, 8, 15, 14, 12, 12, 15, 8, 11, 10, 8, 11, 9, 10, 7, 7, 10, 18, 11, 10, 5, 7, 12, 9, 9, 12, 7, 10, 14, 7, 11, 9, 10, 14, 5, 11, 7, 6, 7, 6, 12, 9, 15, 9, 13, 10, 7, 12, 13, 7, 6, 14, 9, 7, 15, 12, 8, 6, 9, 10, 12, 12, 13, 8, 11, 6, 13, 7, 7, 11, 10, 9, 9, 12, 6, 9, 12, 12, 3, 12, 12, 11, 7, 8, 9, 12, 7, 4, 13, 5, 7, 8, 6, 14, 5, 14, 15, 14, 10, 12, 12, 11, 5, 16, 9, 7, 11, 12, 293628, 7, 10, 7, 12, 7, 7, 8, 9, 8, 8, 7, 7, 2, 14, 10, 15, 18, 12, 5, 12, 15, 10, 11, 8, 8, 14, 14059, 10, 5, 9, 11, 5, 7, 7, 15, 12, 6, 7, 10, 13, 13, 11, 11, 8, 12, 10, 11, 11, 13, 11, 13, 13, 9, 12, 8, 7, 10, 8, 15, 5, 11, 4, 12, 6, 11, 11, 6, 11, 9, 10, 7, 10, 13, 10, 3, 12, 13, 11, 13, 10, 14, 12, 9, 10, 7, 9, 11, 14, 9, 7, 8, 12, 10, 5, 12, 15, 11, 12, 11, 9, 9, 7, 12, 8, 8, 8, 11, 15, 12, 9, 9, 8, 11, 8, 11, 9, 12, 7, 11, 13, 14, 9, 13, 8, 10, 13, 10, 13, 10, 13, 7, 12, 11, 12, 7, 7, 15, 8, 7, 8, 12, 12, 12, 8, 8, 9, 12, 8, 6, 4, 11, 11, 11, 9, 8, 4, 9, 15, 12, 7, 12, 10, 13, 8, 11, 6, 5, 6, 14, 8, 10, 11, 9, 15, 5, 8, 16, 14, 11, 9, 5, 13, 12, 7, 9, 7, 8, 8, 11, 11, 9, 10, 12, 12, 12, 13, 12, 4, 6, 13, 10, 6, 14, 12, 12, 11, 9, 3, 6, 13, 11, 7, 3, 8, 11, 9, 11, 4, 7, 11, 15, 9, 12, 5, 6, 9, 12, 9, 15, 10, 9, 10, 10, 15, 15, 5, 10, 14, 8, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{11, 8, 9, 10, 9, 11, 7, 7, 7, 10, 11, 6, 12, 10, 6, 10, 9, 6, 8, 7, 8, 5, 9, 12, 7, 9, 9, 10, 6, 11, 7, 11, 8, 8, 7, 10, 12, 13, 9, 13, 10, 6, 7, 8, 8, 7, 11, 10, 7, 7, 10, 11, 11, 7, 6, 12, 8, 8, 12, 7, 9, 8, 5, 7, 7, 6, 6, 10, 9, 12, 10, 8, 10, 8, 9, 12, 13, 5, 10, 6, 10, 6, 11, 11, 2, 6, 9, 8, 7, 7, 6, 16, 8, 10, 5, 5, 9, 9, 6, 7, 9, 11, 10, 11, 8, 9, 11, 9, 9, 5, 8, 6, 9, 5, 8, 9, 10, 8, 10, 8, 9, 7, 6, 12, 8, 13, 8, 6, 8, 10, 12, 6, 12, 9, 8, 5, 6, 7, 10, 12, 7, 9, 9, 9, 18, 9, 10, 9, 12, 7, 14, 9, 8, 6, 11, 15, 9, 5, 8, 12, 12, 7, 16, 7, 7, 9, 11, 7, 12, 6, 10, 4, 7, 8, 11, 4, 8, 9, 8, 10, 12, 8, 6, 10, 7, 9, 9, 6, 11, 6, 7, 9, 10, 9, 5, 12, 13, 17, 13, 10, 10, 7, 12, 8, 6, 9, 8, 6, 12, 8, 7, 12, 11, 9, 10, 12, 11, 14, 7, 10, 9, 11, 9, 11, 7, 6, 8, 7, 7, 6, 5, 8, 4, 8, 9, 10, 8, 10, 10, 9, 12, 7, 9, 9, 7, 8, 6, 12, 7, 13, 5, 6, 7, 11, 8, 11, 9, 10, 9, 6, 15, 11, 6, 8, 7, 6, 10, 11, 14, 8, 11, 6, 8, 11, 12, 10, 6, 7, 10, 8, 8, 6, 11, 4, 8, 9, 11, 10, 11, 9, 10, 12, 11, 9, 11, 10, 9, 11, 6, 10, 6, 12, 14, 6, 10, 9, 8, 12, 9, 10, 10, 9, 8, 5, 11, 9, 12, 6, 11, 11, 8, 7, 12, 7, 12, 15, 10, 11, 10, 12, 7, 8, 6, 5, 9, 7, 8, 8, 14, 6, 10, 5, 6, 8, 7, 5, 13, 9, 10, 10, 6, 11, 12, 8, 13, 10, 8, 11, 7, 8, 9, 10, 5, 10, 13, 9, 9, 8, 8, 11, 10, 12, 10, 12, 7, 5, 11, 5, 10, 7, 6, 7, 13, 9, 10, 7, 13, 7, 7, 10, 9, 11, 10, 9, 6, 8, 7, 8, 9, 10, 9, 9, 9, 9, 10, 8, 18, 7, 10, 9, 7, 9, 8, 10, 7, 7, 11, 9, 10, 11, 9, 11, 10, 12, 5, 7, 9, 7, 10, 9, 16, 12, 9, 17, 12, 6, 11, 8, 6, 10, 10, 8, 12, 13, 9, 8, 7, 5, 7, 7, 8, 18, 9, 11, 9, 9, 74236532, 12, 11, 11, 12, 8, 7, 5, 12, 3, 9, 14, 9, 10, 6, 6, 9, 10, 6, 8, 9, 6, 10, 5, 10, 10, 17, 8, 12, 10, 8, 12, 2, 7, 6, 7, 12, 12, 11, 5, 13, 9, 8, 18, 9, 10, 10, 11, 11, 12, 4, 11, 7, 12, 10, 7, 13, 9, 6, 15, 12, 8, 11, 10, 13, 12, 7, 9, 12, 11, 7, 6, 5, 7, 8, 7, 7, 9, 10, 10, 12, 8, 12, 5, 6, 7, 6, 8, 7, 9, 6, 6, 10, 9, 17, 15, 11, 9, 8, 8, 7, 6, 4, 12, 8, 5, 10, 7, 7, 9, 6, 8, 7, 10, 9, 9, 7, 8, 8, 8, 10, 5, 12, 10, 6, 8, 7, 7, 12, 9, 8, 8, 8, 9, 11, 7, 5, 11, 7, 9, 8, 8, 9, 6, 9, 8, 9, 6, 9, 9, 8, 10, 6, 7, 6, 13, 8, 3, 14, 6, 8, 9, 7, 6, 9, 10, 11, 5, 10, 11, 8, 11, 5, 8, 15, 7, 6, 9, 5, 11, 14, 12, 7, 9, 7, 17, 14, 9, 8, 6, 12, 10, 11, 9, 9, 5, 11, 10, 12, 9, 11, 9, 7, 7, 8, 10, 9, 9, 11, 13, 11, 10, 9, 13, 15, 5, 11, 6, 9, 12, 7, 8, 10, 10, 4, 8, 8, 6, 12, 10, 11, 5, 13, 11, 7, 9, 5, 5, 7, 15, 12, 7, 8, 6, 10, 6, 10, 10, 17, 7, 12, 7, 8, 17, 10, 13, 9, 9, 7, 9, 9, 6, 12, 7, 12, 12, 9, 10, 15, 7, 10, 7, 9, 7, 7, 6, 8, 17, 11, 6, 10, 12, 12, 8, 7, 8, 8, 10, 9, 10, 8, 8, 5, 8, 8, 6, 9, 8, 11, 10, 6, 6, 8, 11, 6, 11, 11, 11, 6, 9, 9, 5, 16, 5, 9, 9, 14, 11, 8, 11, 6, 11, 11, 10, 7, 8, 6, 11, 12, 11, 8, 8, 15, 5, 10, 6, 12, 5, 9, 6, 9, 8, 5, 11, 7, 7, 9, 7, 8, 8, 12, 10, 10, 10, 11, 11, 6, 4, 6, 9, 12, 8, 13, 11, 6, 8, 9, 10, 12, 11, 10, 10, 13, 11, 10, 10, 5, 10, 9, 13, 5, 2, 7, 9, 9, 9, 7, 11, 17, 11, 7, 7, 7, 6, 13, 7, 10, 12, 10, 9, 9, 6, 11, 7, 9, 9, 18, 12, 10, 11, 7, 9, 15, 13, 7, 4, 5, 7, 11, 9, 12, 12, 13, 10, 10, 10, 12, 6, 14, 8, 8, 6, 5, 9, 7, 13, 12, 8, 10, 8, 7, 8, 8, 10, 6, 8, 12, 15, 8, 8, 5, 6, 10, 8, 10, 10, 10, 7, 6, 11, 8, 10, 8, 9, 12, 7, 7, 6, 4, 6, 7, 7, 13, 8, 9, 9, 5, 8, 11, 7, 14, 5, 5, 6, 6, 8, 9, 5, 6, 8, 6, 10, 11, 8, 9, 8, 8, 10, 7, 8, 6, 8, 5, 12, 17, 11, 7, 4, 14, 9, 10, 10, 7, 6, 11, 7, 16, 18, 8, 9, 11, 9, 10, 9, 6, 10, 8, 11, 9, 7, 8, 6, 9, 7, 6, 12, 9, 9, 7, 13}

Returns: {-1 }
{10, 5, 10, 9, 13, 8, 11, 12, 9, 19297647, 11, 11, 7, 9, 8, 6, 8, 7, 8, 9, 12, 8, 7, 6, 5, 12, 11, 10, 6, 9, 7, 10, 7, 12, 12, 11, 9, 12, 12, 8, 13, 7, 9, 8, 10, 9, 8, 10, 9, 8, 11, 9, 8, 8, 10, 967067, 10, 10, 11, 7, 10, 7, 10, 8, 14, 11, 11, 6, 9, 10, 10, 5, 7, 8, 7, 10, 8, 10, 9, 10, 10, 13, 8, 7, 10, 5, 10, 6, 7, 11, 7, 13, 9, 5, 12, 10, 8, 8, 9, 9, 12, 9, 4, 2023, 8, 8, 11, 5, 12, 12, 10, 6, 12, 11, 7, 14, 10, 4, 10, 8, 15, 5, 9, 10, 9, 8, 10, 6, 13, 10, 6, 16, 8, 6, 8, 7, 12, 5921, 11, 8, 5, 12, 7, 11, 9, 8, 15, 7, 8, 18766830, 8, 12, 16, 7, 9, 10, 11, 10, 11, 9, 15, 10, 5, 8, 11, 10, 9, 10, 8, 7, 6, 11, 7, 10, 8, 7, 10, 8, 16, 11, 10, 10, 7, 10, 9, 11, 10, 7, 15, 11, 9, 11, 6, 6, 10, 10, 13, 11, 10, 12, 11, 8, 10, 10, 12, 6, 5, 9, 7, 12, 7, 12, 7, 7, 9, 9, 10, 8, 9, 7846, 7, 91083, 9, 16, 9, 8, 8, 11, 8, 10, 110256, 11, 7, 8, 7, 8, 8, 10, 6, 7, 10, 13, 2, 7, 13, 7, 12, 11, 8, 11, 8, 7, 9, 12, 12, 6, 7, 4, 11, 12, 13, 11, 7, 10, 6, 5, 12, 10, 8, 6, 6, 9, 12, 13, 5, 12, 5, 11, 15, 7, 15, 8, 7, 8, 15, 12, 8, 10, 10, 11, 9, 12, 10, 9, 9, 14, 8, 11, 15, 11, 6, 13, 14, 12, 7, 16, 9, 6, 5, 8, 10, 11, 16, 7, 12, 14, 8, 6, 8, 6, 13, 7, 7, 1393171, 6, 13, 4, 6, 5, 10, 7, 11, 9, 11, 13, 10, 6, 9, 6, 6, 74937, 14, 9, 5, 8, 5, 9, 11, 4, 9, 6, 14, 7, 9, 10, 12, 3, 13, 9, 11, 11, 10, 8, 7, 7, 10, 11, 13, 8, 12, 6, 8, 9, 12, 7, 12, 7, 9, 7, 10, 9, 7, 10, 15, 7, 8, 10, 6, 5, 7, 15, 2, 8, 12, 5, 7, 10, 10, 6, 14, 11, 11, 10, 9, 6, 11, 6, 12, 7, 10, 8, 10, 15, 9, 9, 10, 5, 6, 11, 9, 6, 10, 11, 7, 6, 8, 7, 8, 8, 12, 12, 10, 6, 9, 15, 3, 5, 10, 12, 4, 10, 11, 15, 6, 10, 10, 6, 6, 10, 11, 10, 7, 8, 9, 10, 11, 8, 7, 7, 10, 11, 11, 9, 12, 9, 12, 9, 5, 7, 7, 7, 11, 10, 9, 9, 10, 8, 6, 8, 8, 12, 10, 6, 8, 10, 4, 12, 13, 7, 7, 301843, 9, 14, 8, 8, 7, 11, 15, 9, 10, 222094985, 6, 6, 8, 12, 8, 7, 11, 10, 15, 8, 10, 8, 10, 9, 7, 14, 5, 12, 10, 13, 9, 13414093, 250112, 12, 10, 15, 16, 7, 10, 6, 8, 7, 5, 5, 7, 10, 8, 9, 9, 9, 10, 11, 911163, 6, 8, 7, 6, 14, 8, 6, 8, 6, 8, 7, 9, 14, 9, 311278, 15, 7, 9, 10, 26063985, 8, 10, 7, 10, 10, 7, 8, 12, 8, 7, 9, 1587148, 2, 7, 7, 12, 10, 5, 5, 14, 8, 14, 5, 9, 9, 10, 10, 9, 8, 10, 3558, 7, 5, 7, 10, 13, 10, 6, 12, 9, 7, 11, 7, 11, 7, 14, 9, 8, 10, 7, 4522, 9, 10, 6, 10, 11, 8, 10, 8, 8, 9, 7, 6, 8, 12, 10, 5, 11, 13, 896898, 6, 7, 11, 15, 8, 8, 7, 13, 6, 8, 10, 7, 5, 10, 11, 10, 6, 10, 4656919, 11, 11, 10, 10, 7, 11, 8, 10, 7, 7, 13, 11, 8, 10, 12, 983936, 6, 11, 10, 10, 9, 16, 13, 6, 6, 10, 13, 12, 9, 8, 11, 8, 8, 11, 8, 5, 8, 13, 6, 5, 11, 13, 5, 11, 5, 6, 9, 9, 11, 9, 7, 9, 8, 8, 12, 122296, 10, 12, 7, 4, 8, 8, 16, 8, 10, 10, 11, 7, 11, 13, 10, 10, 7, 7, 7, 15, 8, 6, 6, 11, 8, 6, 7, 13, 15, 14, 7, 8, 4, 6, 10, 13, 9, 6, 8, 12, 2880, 12, 11, 11, 11, 76603, 6, 6, 10, 9, 11, 7, 11, 15, 235977, 10, 9, 9, 6, 13, 14, 6, 12, 5, 10, 4, 10, 11, 9, 9, 11, 5, 8, 7, 9, 6, 8, 10, 7, 8, 6, 9, 10, 11, 11, 8, 9, 12, 10, 7, 8, 9, 11, 8, 4, 11, 11, 11, 10, 7, 6, 8, 8, 10, 8, 9, 11, 6, 9, 5, 15, 11, 11, 7, 7, 11, 8, 11007492, 10, 14, 9, 9, 10, 9, 9, 9, 9, 9387, 10, 13, 11, 11, 11, 16, 7, 4, 10, 10, 8, 10, 6, 5, 5, 11, 9, 13, 9, 7, 9, 7, 6, 7, 10, 9, 3447, 7, 128753326, 6, 12, 10, 11, 10, 8, 8, 11, 10, 9, 7, 11, 14, 8, 11, 10, 10, 10, 7, 4, 15, 14, 7, 8, 6, 6, 8, 6, 57548, 8, 7, 7, 8, 8, 8, 8, 8, 4959920, 8, 10, 11, 12, 16, 7, 11, 8, 11, 12, 9, 13325595, 10, 6, 6, 15, 11, 10, 3, 11, 8, 56955948, 10, 10, 8, 7, 6, 15, 6, 10, 12, 10, 10, 6, 10, 11, 8, 8, 8, 12, 10, 11, 9, 8, 698178, 10, 7, 11, 11, 7, 8, 15, 11, 9, 8, 6, 9, 8, 12, 7, 11, 4, 9, 11, 6, 11, 9, 11, 9, 5, 8, 5, 8, 9, 16, 10, 10, 11, 9, 7, 9, 10, 324923521, 7, 8, 9, 6, 7, 6, 8, 6, 11}

Returns: {2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 8, 10, 4, 9, 6, 7, 8, 10, 6, 8, 8, 8, 11, 10, 7, 7, 9, 11, 10, 10, 5, 10, 6, 9, 12, 12, 6, 9, 5, 5, 9, 8, 10, 9, 7, 11, 6, 8, 7, 7, 8, 9, 7, 5, 12, 9, 4, 10, 5, 7, 9, 9, 5, 7, 9, 11, 5, 10, 11, 11, 10, 10, 6, 4, 9, 11, 11, 11, 8, 7, 9, 10, 12, 10, 6, 10, 5, 11, 12, 12, 12, 8, 6, 5, 8, 7, 5, 12, 8, 7, 8, 6, 9, 8, 11, 10, 4, 5, 12, 9, 6, 6, 11, 9, 3, 7, 8, 7, 7, 11, 8, 14, 9, 7, 11, 8, 9, 6, 9, 9, 8, 8, 7, 10, 8, 6, 8, 4, 9, 9, 7, 10, 11, 8, 8, 7, 8, 10, 6, 10, 7, 9, 12, 5, 11, 7, 9, 8, 9, 12, 7, 9, 8, 10, 12, 8, 11, 8, 6, 6, 9, 11, 12, 8, 7, 9, 52274862, 13, 7, 8, 6, 5, 7, 11, 6, 9, 9, 7, 5, 10, 9, 9, 8, 10, 7, 13, 11, 8, 11, 9, 6, 10, 10, 10, 7, 6, 7, 9, 4, 11, 6, 6, 302947163, 8, 8, 8, 11, 9, 13, 13, 6, 8, 9, 5, 10, 7, 9, 7, 8, 11, 6, 11, 7, 9, 14, 8, 7, 9, 9, 4, 8, 7, 8, 7, 7, 9, 9, 4, 5, 4, 8, 7, 7, 8, 7, 8, 5, 9, 9, 8, 11, 8, 9, 12, 6, 11, 7, 9, 9, 7, 8, 8, 7, 8, 8, 10, 10, 10, 10, 8, 6, 10, 8, 9, 13, 8, 6, 11, 6, 7, 6, 8, 9, 6, 9, 10, 9, 6, 9, 12, 5, 10, 5, 11, 9, 11, 9, 8, 9, 3, 8, 4, 6, 9, 10, 11, 5, 10, 7, 10, 8, 10, 12, 6, 10, 11, 8982, 6, 5, 10, 8, 272048799, 6, 6, 8, 13, 8, 11, 8, 11, 8, 10, 7, 116721, 7, 10, 9, 5, 6, 8, 8, 10, 6, 10, 9, 7, 6, 6, 5, 9, 8, 8, 12, 9, 12, 10, 6, 7, 9, 10, 10, 10, 8, 12, 277795, 8, 10, 7, 10, 6, 8, 9, 10, 8, 11, 4, 13, 11, 9, 10, 13, 9, 3, 7, 8, 9, 8, 10, 8, 6, 8, 6, 11, 7, 10, 9, 6, 11, 11, 9, 6, 6, 6, 13, 5, 8, 9, 11, 4, 7, 12, 11, 8, 9, 10, 5, 7, 7, 9, 10, 10, 8, 8, 9, 6, 11, 12, 7, 9, 8, 10, 7, 7, 12, 7, 6, 8, 11, 5, 12, 8, 8, 9, 8, 8, 5, 9, 7, 6, 11, 7, 8, 7, 8, 6, 8, 9, 9, 12, 7, 6, 22366, 9, 11, 7, 8, 12, 9, 11, 5, 7, 12, 7, 11, 9, 7, 7, 8, 9, 5, 8, 8, 8, 8, 12, 11, 8, 7, 8, 13, 10, 5, 13, 11, 6, 10, 5, 12, 11, 9, 10, 8, 6, 13, 8, 8, 10, 10, 7, 13, 9, 12, 9, 11, 6, 8, 9, 10, 8, 4, 11, 8, 8, 8, 8, 11, 11, 8, 9, 5, 9, 8, 6, 5, 9, 8, 6, 10, 9, 12, 8, 11, 7, 8, 9, 12, 5, 7, 7, 5, 13, 5, 6, 10, 6, 10, 4, 13, 11, 14, 12, 8, 9, 10, 8, 6, 7, 8, 10, 5, 8, 13, 8, 12, 7, 9, 8, 8, 78945, 10, 10, 6, 11, 10, 5, 8, 8, 13, 10, 11, 8, 8, 6, 11, 13, 7, 7, 8, 9, 8, 7, 6, 8, 9, 9, 8, 12, 9, 7, 7, 12, 12, 6, 8, 10, 5, 11, 8, 5, 10, 13, 8, 10, 6, 4, 9, 11, 10, 12, 4, 5, 11, 7, 12, 8, 11, 6, 5, 11, 11, 13, 11, 6, 8, 6, 9, 13, 6, 6, 13, 7, 12, 10, 11, 8, 10, 9, 10, 5, 10, 8, 10, 9, 9, 7, 7, 11, 7, 7, 8, 8, 6, 8, 8, 6, 6, 8, 5, 5, 7, 11, 10, 8, 7, 4, 7, 8, 13, 4, 8, 10, 10, 8, 9, 7, 7, 7, 12, 9, 6, 6, 3, 8, 8, 7, 6, 8, 6, 8, 5, 7, 6, 8, 6, 8, 4, 10, 8, 9, 6, 5, 7, 6, 10, 8, 10, 11, 8, 8, 9, 9, 12, 11, 8, 9, 9, 10, 11, 9, 9, 8, 7, 9, 8, 8, 10, 8, 7, 6, 7, 4, 7, 7, 8, 8, 5, 11, 10, 10, 11, 6, 11, 7, 10, 12, 11, 6, 7, 11, 12, 9, 6, 12, 10, 13, 10, 7, 9, 7, 9, 6, 10, 12, 11, 11, 9, 6, 7, 7, 10, 5, 12, 6, 9, 5, 10, 9, 9, 8, 7, 8, 8, 6, 8, 12, 8, 9, 8, 12, 8, 8, 8, 12, 11, 13, 10, 9, 8, 6, 9, 6, 10, 12, 9, 10, 5, 10, 11, 10, 6, 9, 10, 8, 7, 5, 5, 10, 6, 12, 10, 11, 9, 10, 6, 7, 10, 6, 13, 7, 6, 11, 6, 8, 6, 6, 7, 7, 7, 1428, 8, 5, 3, 6, 10, 8, 5, 6, 5, 6, 10, 10, 13, 10, 8, 6, 10, 11, 6, 9, 8, 7, 12634, 6, 9, 6, 4, 4, 5, 9, 9, 7, 8, 9, 8, 8, 7, 9, 12, 12, 9, 4, 8, 13, 9, 9, 9, 8, 11, 12, 10, 8, 5, 8, 6, 6, 8, 6, 7, 8, 10, 12, 7, 8, 9, 11, 7, 4, 8205, 9, 12, 6, 12, 8, 11, 12, 8, 9, 8, 7, 9, 6, 9, 4, 7, 9, 6, 11, 10, 6, 5, 8, 9, 8, 12, 5, 7, 7, 10, 9, 5, 7, 9, 8, 11, 11, 8, 10, 10, 7, 9, 12, 10, 8, 10, 9, 10, 8, 9, 13, 7, 7, 6, 12, 7, 12}

Returns: {2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 10, 7, 12, 5, 5, 10, 8, 10, 8, 5, 12, 6, 8, 9, 8, 11, 9, 10, 9, 9, 14, 8, 13, 10, 9, 12, 9, 7, 8, 8, 10, 7, 8, 12, 8, 10, 6, 8, 10, 8, 9, 6, 7, 12, 7, 6, 5, 434732170, 8, 10, 5, 9, 12, 11, 7, 10, 7, 9, 5, 9, 10, 10, 6, 7, 10, 11, 6, 9, 9, 6, 4, 7, 6, 8, 8, 11, 6, 9, 7, 10, 8, 9, 7, 7, 10, 10, 9, 8, 8, 7, 6, 7, 12, 4, 9, 9, 10, 8, 13, 10, 8, 6, 7, 7, 10, 9, 11, 8, 11, 9, 10, 7, 8, 10, 8, 13, 8, 6, 7, 9, 10, 5, 10, 5, 6, 8, 10, 8, 3, 5, 3674, 11, 7, 4, 5, 1217064, 11, 12, 6, 9, 3, 12, 7, 7, 14, 6, 7, 10, 8, 6, 11, 8, 9, 7, 12, 13, 9, 13, 8, 10, 9, 9, 5, 6, 7, 6, 11, 9, 6, 5, 7, 8, 9, 9, 4, 9, 4090424, 10, 6, 8, 9, 169866, 10, 10, 10, 7, 7, 9, 6, 10, 7, 8, 13, 7, 5, 8, 10, 8, 10, 5, 7, 9, 6, 11, 11, 13, 8, 7, 8, 10, 8, 8, 9, 10, 10, 6, 10, 9, 9, 9, 10, 11, 10, 6, 11, 3, 9, 11, 8, 7, 8, 8, 8, 7, 5, 9, 7, 12, 8, 10, 9, 9, 8, 11, 8, 5, 10, 10, 7, 5, 11, 9, 11, 9, 9, 9, 10, 13, 6, 4, 11, 13, 5, 9, 5, 7, 10, 11, 9, 6, 9, 12, 7, 8, 10, 10, 12, 6, 6, 10, 7, 7, 6, 8, 12, 8, 12, 9, 10, 10, 81583848, 12, 6, 10, 5, 8, 7, 12, 9, 9, 12, 8, 8, 9, 9, 9, 14, 10, 7, 10, 12, 12, 10, 14, 8, 7, 8, 6, 7, 8, 7, 12, 5, 9, 8, 24508, 8, 4, 9, 10, 10, 9, 10, 11, 8, 10, 5, 8, 10, 5, 7, 8, 7, 6, 8, 8, 9, 8, 7, 10, 10, 4, 9, 11, 6, 11, 12, 8, 9, 6, 9, 8, 8, 7, 7, 8, 7, 9, 9, 11, 12, 10, 8, 8, 6, 11, 11, 10, 9, 7, 11, 7, 13, 7, 7, 8, 10, 13, 11, 10, 10, 7, 13, 11, 9, 7, 9, 6, 12, 7, 8, 11, 10, 8, 10, 5, 10, 10, 9, 7, 7, 9, 10, 6, 8, 10, 9, 12, 6, 8, 10, 10, 7, 7, 7, 10, 10, 11, 9, 12, 10, 7, 9, 8, 9, 10, 9, 10, 1515, 11, 8, 5, 10, 6, 9, 9, 8, 11, 6, 9, 10, 7, 8, 10, 7, 8, 10, 4, 7, 8, 8, 10, 6, 9, 10, 7, 9, 5, 9, 12, 9, 10, 9, 12, 10, 9, 168063279, 8, 8, 11, 12, 11, 8, 6, 9, 7, 3, 9, 6, 11, 12, 6, 10, 8, 7, 9, 6, 2422979, 9, 8, 9, 7, 10, 6, 8, 5, 11, 10, 8, 9, 14, 10, 11, 5, 10, 8, 8, 7, 11, 8, 10, 11, 8, 9, 11, 5, 11, 9, 10, 8, 7, 13, 8, 2, 11, 11, 12, 7, 7, 10, 11, 9, 6, 9, 10, 11, 7, 10, 10, 6, 9, 9, 8, 9, 9, 12, 11, 7, 10, 5, 10, 7, 11, 9, 9, 8, 6, 4, 5, 10, 8, 8, 12, 9, 3, 7, 8, 9, 10, 5, 11, 7, 9, 7, 9, 9, 9, 7, 9, 7, 8, 6, 13, 5, 7, 7, 7, 8, 10, 7, 11, 10, 12, 9, 10, 4, 9, 7, 9, 9, 8, 12, 17943, 7, 12, 9, 10, 7, 10, 8, 13, 8, 4, 8, 9, 7, 9, 6, 9, 5, 8, 7, 116554, 10, 11, 7, 11, 8, 10, 12, 8, 7, 9, 9, 9, 10, 8, 8, 5, 9, 10, 7, 9, 7, 8, 10, 7, 8, 9, 7, 7, 8, 7, 9, 7, 8, 1897399, 9, 6, 8, 9, 8, 6, 7, 9, 7, 11, 8, 11, 123363, 8, 7, 8, 14, 11, 6, 8, 8, 9, 8, 12, 9, 263584681, 9, 8, 7, 9, 8, 7, 8, 12, 7, 9, 9, 9, 9, 10, 6, 7, 11, 13, 6, 8, 12, 10, 10, 6, 13, 8, 10, 10, 8, 9, 9, 7, 6, 8, 4, 9, 13, 7, 7, 11, 10, 8, 9, 9, 12, 7, 8, 9, 262746, 8, 7, 12, 7, 11, 7, 7, 11, 9, 10, 10, 7, 5, 9, 9, 10, 8, 9, 10, 9, 11, 10, 10, 8, 7, 10, 9, 9, 6, 4, 10, 8, 10, 7, 11, 11, 3355, 12, 10, 10, 6, 9, 12, 8, 9, 5, 10, 8, 11, 10, 11, 7, 5, 12, 5, 10, 8, 9, 12, 8, 12, 5, 12, 8, 5, 10, 12, 10, 10, 10, 9, 7, 12, 9, 8, 10, 8, 6, 12, 4, 8, 9, 11, 5, 11, 7, 10, 10, 10, 9, 10, 8, 6, 4, 9, 8, 9, 10, 9, 12934, 8, 11, 9, 13, 7, 7, 11, 8, 7, 4, 8, 5, 9, 10, 9, 8, 8, 8, 6, 7, 13, 9, 10, 7, 6, 10, 10, 9, 7, 6, 10, 8, 11, 8, 8, 9, 9, 12, 12, 8, 11, 8, 7, 7, 7, 10, 5, 10, 11, 7, 6, 9, 9, 12, 9, 11, 7, 10, 7, 9, 13, 7, 8, 12, 9, 9, 9, 10, 8, 11, 10, 8, 9, 6, 9, 9, 8, 10, 12, 12, 8, 3, 3, 10, 3, 10, 11, 5, 7, 9, 6, 11, 11, 12, 395939723, 10, 7, 8, 9, 6, 8, 8, 11, 9, 9, 8, 11, 8, 11, 6, 11, 6, 10, 10, 6, 9, 9, 9, 9, 9, 5, 6, 9, 9, 8, 6, 10, 9, 10, 17173298, 6, 9, 9, 9, 13, 7, 9, 10, 6, 10, 10, 8, 8, 10, 7, 13210, 8}

Returns: {2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{9, 7, 6, 8, 7, 7, 9, 5, 9, 8, 13, 8, 8, 7, 9, 11, 10, 21359912, 16, 15, 11, 8, 5, 6, 6, 20520, 15, 9, 8, 10, 13, 10, 5, 8, 6, 11, 15, 4, 9, 3, 15, 7, 10, 11, 16, 8, 6, 13, 5, 7, 4103, 14, 14, 13, 5, 6, 4, 10, 13, 15, 11, 14, 11, 12, 12, 14, 7, 11, 9, 9, 17, 17, 19, 15, 4547, 5, 14, 10, 8, 6, 12, 8, 8, 10, 16, 9, 14, 4162465, 13, 7, 7, 4, 4, 17, 11, 7, 11, 11, 6, 7, 12, 8, 15, 15, 5, 5, 12, 18, 15, 7, 10, 16, 6, 17, 6, 15, 8, 11, 15, 9, 11, 4, 13, 10, 137696706, 12, 11, 6, 14, 11, 11, 15, 7, 15, 16, 8, 11, 13, 7, 7, 6, 13, 116452, 17, 44199728, 6, 12, 7, 11, 9, 4, 10, 7, 7, 5, 8, 6, 9, 7, 13, 6, 8, 5, 8, 10, 9, 7, 16, 9, 7, 14, 11, 168134256, 18, 10, 12, 5, 10, 17, 7, 8, 12, 12, 10, 10, 7, 8, 8, 15, 9, 15, 12, 13, 12, 17, 7, 8, 8, 13, 8, 14, 6, 8, 8, 7, 14, 12, 7, 12, 12, 7, 17, 16, 7, 12, 9, 11, 8, 5, 13, 10, 8, 9, 8, 5, 4, 7, 4, 8, 6, 12, 9, 10, 17, 13434100, 14, 6, 6, 7, 9, 10, 11, 3, 12, 13, 12, 8, 7, 18, 8, 12, 9, 8, 6, 9, 7, 7, 8, 6, 14, 8, 9, 11, 11, 8, 9, 16, 5, 11, 12, 8, 6, 5, 4, 6, 10, 12, 6, 11, 15, 13, 12, 14, 9, 6, 9, 9, 4, 11, 4, 6, 7, 11, 5, 14, 14, 16, 5, 7, 11, 13, 6, 7, 3, 5, 8, 7, 8, 12, 7, 7, 9, 13, 158892, 12, 16, 6, 9, 12, 14, 14, 13, 11, 11, 14, 6, 13, 9, 6, 10, 12, 9, 11, 16, 9, 16, 12, 12, 14, 11, 7, 13, 17, 5, 13, 8, 10, 7, 8, 172580, 8, 12, 13, 6, 6, 8, 5, 13, 17, 8, 7, 5, 13, 8, 9, 10, 14, 7, 14, 8, 14, 11, 12, 12, 7, 5, 12, 15, 17, 12, 8, 9, 13, 9, 10, 7, 7, 15, 17, 7, 8, 13, 6, 6, 16, 9, 12, 16, 10, 5, 5, 10, 5, 9, 6, 9, 15, 15, 9, 8, 9, 4, 9, 10, 10, 7, 7, 14, 10, 4, 9, 11, 11, 12, 15, 15, 12, 17, 15, 14, 13, 7, 9, 9, 7, 9, 4, 6, 92310, 8, 12, 14, 15, 9, 10, 18, 8, 4, 10, 8, 13, 5, 7, 8, 6, 4, 9, 8, 13, 7, 6, 12, 6, 15, 8, 13, 9, 15, 16, 12, 14, 11, 16, 15, 10, 5, 10, 17, 7, 7, 10, 10, 15, 12, 5, 15, 9, 7, 219246, 11, 15, 17, 13, 12, 12, 8, 6, 14, 8, 5, 7, 1764, 12, 11, 5, 120969114, 11, 6, 9, 6, 13, 12, 11, 17, 13, 14, 8, 15, 5, 5, 17, 9, 11, 8, 6, 42625, 15, 11, 8, 5, 4, 13, 8, 11, 6, 7434610, 17, 16, 15, 6, 8, 5, 10, 8, 4, 11, 8, 13, 11, 1512, 8, 5, 7, 17, 4, 6, 5, 12, 8, 11, 6, 7, 8, 7, 7, 13, 6, 17, 10, 9, 11, 15, 8, 8, 16, 7, 18, 8, 9, 11, 13, 14, 8, 5, 9, 9, 8, 14, 7, 12, 8, 16, 5, 6, 8, 9, 6, 5, 6, 11, 9, 15, 9, 7, 8, 7, 11, 9, 6, 7, 10, 135079244, 6, 5, 7, 16, 8, 13, 7, 12, 19, 13, 7, 6, 9, 7, 12, 6, 9, 13, 8, 9, 14, 8, 7, 42177561, 11, 12, 15, 8, 15, 7, 6, 12, 14, 11, 9, 6, 8, 12, 9, 7, 4, 9, 7, 6, 5, 8, 6, 7, 17, 6, 7, 11, 13, 14, 7, 5, 8, 5, 6, 7, 10, 46167, 8, 7, 9, 11, 4, 8, 5, 7, 7, 9, 8, 4, 9, 16, 7, 10, 14, 9, 17, 508466596, 6, 8, 14, 8, 10, 9, 6, 11, 12, 12, 7, 9, 8, 8, 9, 9, 12, 10, 9, 6, 4, 10, 11, 10, 10, 11, 14, 17, 10, 10, 9, 13, 10, 11, 5, 8, 15183659, 9, 17, 14, 8, 13, 14, 9, 8, 9, 10, 7, 17, 15, 9, 7, 6, 5, 15, 13, 6, 13, 15, 11, 11, 9, 13, 6, 12, 13, 11, 10, 13, 16, 10, 15, 14, 5, 11, 9, 11, 12, 8, 14, 11, 6, 7, 15, 5, 9, 12, 10, 11, 6, 9, 8, 11, 5, 6, 9, 10, 12, 8, 17, 7, 14, 13, 7, 7, 1668, 7, 8, 8, 8, 17, 15, 7, 15, 4, 27788148, 9, 7, 17, 12, 10, 9, 16, 10, 6, 8, 2758398, 10, 16, 8, 5, 11, 12, 12, 15, 10, 17, 14, 7, 7, 11, 7, 9, 35550, 9, 8, 8, 7, 8, 12, 7, 184661, 14, 12, 12, 6, 15, 14, 10, 16, 15, 11, 6, 15, 5, 9, 10, 9, 12, 8, 8, 6, 10, 12, 8, 9, 7, 4, 16, 11, 11, 7, 16, 6, 12, 13, 7, 5, 14, 15, 8, 8, 8, 8, 11, 5, 11, 11, 7, 6, 5, 6, 9, 9, 5, 10, 10, 11, 11, 17, 6, 8, 9, 7, 9, 9, 9, 7, 15, 16, 16, 8, 6, 8, 6, 14, 4, 15, 14, 8, 6, 6, 4, 9, 31860, 195280, 17, 6, 6, 14, 14, 14, 11, 10, 12, 7, 9, 16, 6, 12, 415887598, 8, 19, 5, 9, 8, 8, 11, 7, 6, 6, 10, 8, 9, 7, 12, 6, 9, 6, 17, 8, 4, 2, 12, 6, 8, 12, 15, 11, 7, 14, 10, 5, 10, 12, 8, 17}

Returns: {-1 }
{7, 9, 9, 6, 7, 16, 10, 9, 9, 13, 10, 10, 6, 14, 10, 7, 12, 3, 10, 13, 10, 7, 7, 6, 9, 6, 13, 11, 8, 8, 12, 6, 12, 13, 9, 4, 6, 10, 10, 9, 6, 9, 10, 6, 9, 9, 8, 14, 12, 13, 8, 10, 8, 13, 7, 10, 14, 14, 9, 12, 8, 12, 5, 9, 7, 18, 10, 4, 13, 11, 6, 7, 6, 5, 7, 16, 7, 12, 6, 9, 6, 3, 9, 9, 99068, 6, 9, 9, 7, 5, 9, 11, 15, 4, 8, 9, 11, 6, 17, 9, 8, 14, 9, 9, 8, 4, 6, 9, 6, 9, 11, 13, 12, 11, 7, 10, 9, 13, 10, 7, 11, 14, 2, 4, 7, 9, 9, 5, 9, 2647102, 6, 7, 7, 6, 11, 9, 10, 16, 10, 9, 5, 13, 7, 7, 12, 12, 7, 9, 16, 8, 12, 5, 10, 12, 8, 14, 12, 12, 9, 17, 11, 7, 8, 9, 9, 7, 14, 15, 10, 251228, 15, 7, 7, 11, 10, 7, 12, 9, 12, 13, 7, 13, 8, 6, 9, 10, 8, 11, 10, 13, 5, 7, 7, 19, 7, 8, 8, 9, 18, 10, 11, 5, 10, 12, 9, 11, 5, 5, 13, 10, 19, 7, 12, 6, 8, 9, 5, 138315, 11, 6, 11, 8, 7, 6, 4, 10, 5, 1390, 12, 6, 8, 12, 13, 10, 10, 6, 23733, 12, 8, 17, 14, 15, 7, 6, 10, 6, 7, 8, 6, 7, 8, 9, 9, 18, 13, 11, 12, 15, 6, 12, 18, 11, 10, 8, 12, 12, 9, 19, 7, 8, 8, 10, 3, 11, 9, 8, 12, 6, 3, 13, 8, 16, 6, 8, 5, 9, 9, 8, 13, 9, 12, 12, 7, 8, 17, 4, 6, 9, 11, 5, 11, 14, 11, 19, 11, 10, 16, 8, 9, 406216641, 16, 12, 5, 10, 8, 11, 19506, 6, 9, 9, 8, 8, 14, 22646378, 5, 9, 14, 7, 7, 7, 6, 12, 12, 5, 13, 10, 6, 16, 17, 10, 7, 6, 13, 7, 8, 14, 8, 10, 18, 8, 12, 9, 9, 8, 15, 9, 21288663, 19, 9, 5, 7, 8, 9, 9, 9, 7, 8, 5, 8, 14, 7, 9, 12, 6, 8, 4, 11, 9, 7, 9, 9, 8, 6, 8, 12, 6, 18, 6, 12, 6, 12, 13, 11, 9, 7, 8, 15, 7, 7, 85287, 6, 10, 6, 6, 15, 10, 8, 13, 6, 16, 7, 5, 11, 12, 8, 9, 6, 8, 11, 5, 7, 9, 5, 11, 12, 12, 5, 7, 6, 10, 5, 8, 7, 7, 12, 6, 8, 5, 7, 8, 5, 13, 7, 7, 12, 9, 11, 6, 6, 12, 18, 6, 76337, 4, 13, 11, 19, 6, 10, 9, 10, 12, 10, 6, 6, 14, 8, 8, 7, 9, 6, 16, 6, 6, 13, 18, 8, 9, 7, 8, 11, 7, 11, 4, 15, 9, 7, 18, 6, 10, 9, 9, 7, 4, 12, 8, 7, 7, 9, 6, 8, 4, 17, 14, 6, 13, 7, 6, 8, 10, 7, 4, 7, 12, 10, 10, 6, 4, 8, 10, 9, 5, 7, 8, 5, 7, 9, 8, 14, 8, 6, 11, 4, 7, 9, 5, 6, 11, 518050, 9, 9, 10, 9, 4, 8, 11, 10, 15, 8, 6, 16, 5960700, 7, 11, 7, 9, 9, 5, 6, 6, 13, 5, 7, 6, 6, 16, 14, 7, 9, 10, 4, 9, 18, 8, 6, 7, 18, 8, 13, 7, 9, 11, 5, 11, 6, 5, 7, 12, 12, 7, 10, 11, 3252043, 14, 11, 12, 10, 9, 7, 7, 8, 13, 8, 8, 6, 8, 13, 7, 16, 9, 7, 13, 12, 9, 9, 8, 9, 10, 11, 13, 10, 11, 8, 10, 6, 16, 9, 6, 7, 9, 12, 12, 9, 11, 16, 10, 8, 13, 12, 9, 12, 7, 8, 6, 5, 10, 4, 5, 11, 11, 9, 10, 9, 11, 8, 11, 6, 14, 10, 7, 8, 5, 7, 9, 11, 8, 13, 6, 7, 7, 12, 10, 10, 12, 15, 7, 10, 11, 11, 9, 6, 10, 11, 14, 12, 8, 10, 8, 11, 6, 10, 8, 11, 6, 6, 7, 9, 9, 10, 6, 11, 5, 12, 7, 12, 11, 14, 10, 6, 9, 6, 6, 8, 4, 7, 6, 7, 10, 5, 16, 12, 12, 13, 9, 9, 10, 13, 251699, 13, 11, 7, 10, 9, 6, 10, 14, 8, 13, 11, 7, 10, 12, 62136058, 12, 7, 6, 12, 13, 7, 10, 9, 8, 12, 6, 8, 13, 17, 13, 15, 6, 9, 19, 12, 7, 9, 12, 9, 17, 8, 12, 14, 12, 6, 12, 7, 14, 7, 11, 5, 7, 6, 8, 8, 6, 11, 12, 5, 13, 14, 11, 13, 8, 9, 7, 7, 17, 16, 13, 7, 9, 30551436, 9, 9, 7, 11, 12, 7, 9, 13, 6, 4, 6, 6, 9, 6, 11, 14, 4, 12, 15, 6, 4, 14, 7, 11, 7, 6, 9, 6, 8, 6, 5, 12, 7, 8, 6, 7, 9, 12, 6, 17, 9, 4, 8, 12, 6, 6361, 8, 10, 6, 13, 6, 7, 8, 9, 8, 7, 8, 5, 19, 16, 7, 13, 12, 10, 10, 16, 8, 10, 19, 6, 5, 5, 8, 10, 7, 12, 8, 10, 8, 16, 11, 9, 9, 10, 18, 10, 15, 14, 9, 12, 8, 8, 10, 7, 6, 14, 8, 11, 9, 11, 7, 11, 11, 7, 13, 10, 8, 8, 9, 13, 8, 14, 8, 11, 11, 8, 7, 11, 9, 6, 6, 12, 6, 12, 8, 9, 9, 12, 11, 12, 9, 12, 8, 14, 7, 8, 13, 13, 6, 14, 12, 12, 303184716, 8, 6, 9, 9, 8, 5, 12, 10, 8, 8, 6, 16, 13, 7, 7, 13, 14, 10, 6, 8, 12, 7, 4, 5, 15, 11, 9, 6, 10, 8, 9, 6, 16, 6, 8, 12, 5, 8, 10, 11, 10, 13, 9, 6, 6, 11, 8, 7, 5, 13, 6, 9, 10}

Returns: {-1 }
{14, 7, 8, 5, 6, 4, 10, 14, 8, 10, 13, 11, 10, 7, 12, 12, 10, 7, 9, 10, 7, 9, 13, 14, 11, 9, 7, 9, 4, 11, 10, 9, 9, 13, 8, 10, 6, 11, 11, 9, 13, 8, 7, 10, 7, 12, 5, 13, 11, 7, 12, 6, 10, 10, 12, 8, 9, 10, 10, 11, 10, 9, 11, 13, 10, 4, 12, 7, 9, 14, 8, 9, 9, 10, 10, 14, 9, 9, 12, 13, 10, 7, 10, 9, 8, 9, 7, 9, 8, 10, 9, 9, 14, 5, 10, 9, 7, 6, 6, 9, 9, 8, 11, 12, 17518565, 12, 14, 9, 12, 8, 15, 10, 42848, 13, 6, 11, 8, 11, 8, 11, 6, 10, 12, 9, 13, 14, 7, 13, 11, 7, 7, 7, 10, 12, 8, 10, 14, 8, 11, 9, 42124, 10, 11, 10, 9, 15, 7, 12, 10, 14, 6, 14, 6, 7, 6, 9, 9, 3, 9, 6, 7, 12, 7, 2, 9, 8, 10, 8, 13, 13, 7, 6, 11, 9, 10, 8, 9, 12, 12, 9, 7, 9, 13, 10, 10, 10, 10, 8, 10, 13, 6, 10, 10, 9, 11, 12, 11, 9, 2, 11, 13, 14, 7910, 10, 10, 6, 9, 5, 4, 13, 8, 11, 10, 10, 11, 11, 13, 10, 10, 11, 12, 9, 10, 11, 11, 9, 14, 10, 10, 8, 12, 10, 9, 8, 9, 13, 7, 5, 10, 8, 7, 13, 10, 10, 11, 12, 6, 6, 13, 13, 10, 10, 7, 4, 8, 6, 7, 10, 8, 10, 13, 13, 10, 11, 11, 11, 11, 6, 13080, 10, 13, 4, 12, 7, 5, 11, 11, 12, 11, 9, 13, 7, 11, 10, 11, 9, 7, 14, 11, 10, 14, 10, 12, 6, 12, 6, 7, 13, 12, 11, 9, 6, 10, 6, 12, 8, 9, 9, 7, 7, 9, 10, 6, 10, 5, 10, 11, 11, 6, 10, 3, 9, 11, 8, 10, 9, 10, 10, 7, 9, 9, 8, 10, 8, 11, 7, 10, 11, 9, 12, 13, 8, 10, 9, 9, 10, 10, 13, 5, 9, 7, 11, 3, 13, 13, 10, 12, 9, 8, 8, 9, 8, 7, 9, 11, 9, 4, 13, 10, 6, 14, 10, 8, 3, 11, 9, 11, 7, 9, 9, 10, 12, 9, 7, 6, 10, 12, 10, 13, 11, 10, 13, 12, 10, 5, 13, 7, 11, 9, 11, 8, 9, 4, 11, 10, 10, 11, 7, 9, 8, 9, 11, 7, 12, 12, 7, 4, 10, 11, 10, 11, 12, 10, 10, 8, 8, 12, 8, 11, 8, 10, 12, 10, 5, 9, 12, 11, 5, 10, 11, 8, 12, 8, 9, 9, 5, 10, 10, 9, 7, 9, 13, 9, 12, 6, 9, 7, 10, 5, 9, 10, 10, 9, 10, 12, 8, 9, 8, 11, 7, 10, 7, 7, 7, 10, 11, 9, 10, 12, 6, 5, 7, 12, 13, 9, 12, 5, 12, 12, 3, 9, 6, 7, 9, 10, 9, 7, 5, 13, 9, 12, 12, 6, 9, 11, 9, 7, 11, 7, 10, 11, 9, 13, 10, 9, 9, 12, 10, 8, 9, 10, 6, 9, 12, 8, 9, 9, 7, 6, 7, 7, 10, 12, 11, 9, 11, 8, 9, 14, 7, 10, 5, 9, 13, 12, 13, 8, 9, 10, 11, 10, 13, 10, 10, 9, 11, 8, 6, 9, 10, 9, 12, 7, 11, 9, 8, 12, 7, 11, 7, 7, 7, 9, 5, 10, 8, 10, 9, 10, 8, 13, 9, 5, 10, 11, 9, 5, 6, 11, 5, 9, 13, 6, 9, 6, 11, 10, 9, 9, 10, 9, 6, 5, 8, 5, 8, 11, 10, 9, 7, 10, 9, 13, 13, 12, 12, 9, 5, 12, 8, 10, 10, 10, 13, 11, 8, 6, 12, 8, 9, 13, 7, 11, 12, 196655, 10, 9, 9, 10, 7, 14, 7, 5, 7, 9, 12, 7, 10, 9, 9, 12, 6, 10, 6, 9, 11, 3331, 7, 10, 11, 13, 8, 12, 7, 8, 7, 7, 9, 13, 4, 12, 4, 15, 11, 13, 10, 9, 2398065, 10, 13, 10, 8, 6, 13, 15, 10, 10, 8, 14, 12, 9, 7, 10, 11, 9, 10, 10, 8, 12, 9, 14, 13, 13, 13, 13, 7, 8, 6, 11, 8, 9, 6, 4, 9, 4, 13, 7, 7, 12, 8, 13, 7, 9, 10, 8, 13, 8, 11, 7, 10, 11, 3, 9, 10, 9, 7, 10, 8, 4, 13, 11, 6, 12, 8, 9, 6, 9, 11, 4, 8, 12, 10, 6, 10, 11, 9, 6, 6, 11, 10, 9, 8, 12, 10, 8, 10, 5, 12, 11, 9, 6, 7, 11, 12, 13, 8, 9, 6, 11, 11, 11, 12, 7, 9, 12, 13, 5, 10, 10, 6, 9, 9, 5, 12, 12, 9, 4, 7, 11, 7, 10, 8, 8, 8, 7, 7, 6, 9, 7, 12, 6, 5, 7, 4, 7, 6, 12, 7, 8, 9, 8, 7, 11, 5, 7, 10, 3, 10, 9, 9, 6, 9, 9, 9, 7, 12, 10, 9, 6, 12, 11, 7, 9, 9, 9, 9, 7, 9, 10, 6, 11, 9, 13, 13, 11, 6, 7, 13, 13, 12, 10, 6, 14, 9, 9, 12, 8, 10, 11, 13, 9, 9, 11, 385741, 9, 8, 6, 11, 7, 8, 9, 11, 10, 9, 9, 9, 9, 9, 7, 9, 10, 8, 12, 12, 9, 6, 8, 8, 11, 5, 7, 11, 8, 11, 11, 8, 10, 13, 9, 8, 9, 11, 10, 12, 7, 6, 9, 8, 12, 12, 8, 13, 6, 7, 5, 10, 10, 8, 10, 7, 15, 10, 11, 7, 8, 7, 10, 7, 7, 13, 7, 11, 13, 11, 7, 7, 11, 10, 10, 9, 10, 9, 7, 9, 9, 12, 5, 9, 8, 10, 9, 11, 12, 11, 10, 7, 9, 10, 11, 6, 8, 11, 12, 13, 8, 7, 14, 11, 9, 10, 9, 10, 10, 15, 13, 10, 9, 7, 6, 8, 5, 10, 10, 9, 7, 7, 8, 11, 12, 12}

Returns: {-1 }
{9, 9, 11, 15, 8, 7, 9, 11, 13, 7, 8, 14, 9, 12, 8, 15, 11, 12, 11, 8, 3, 8, 307396, 7, 15, 11, 15, 9, 10, 7, 11, 8, 8, 17, 9, 10, 13, 5, 2, 10, 9, 10, 11, 7, 7, 15, 7, 8, 8, 7, 10, 12, 5, 6, 10, 10, 12, 12, 10, 10, 9, 10, 8, 13, 9, 6, 13, 8, 13, 6, 12, 8, 13, 10, 10, 4, 8, 10, 4, 4, 10, 8, 11, 3, 8, 8, 5, 12, 11, 5079, 11, 10, 13, 9, 8, 14, 11, 7, 13, 7, 14, 7, 10, 11, 8, 11, 10, 5, 12, 13, 10, 10, 9, 12, 8, 10, 11, 11, 10, 9, 12, 10, 8, 15, 8, 14, 13, 8, 11, 14, 11, 9, 8, 12, 10, 7, 14, 6, 7, 10, 5, 7, 15, 14, 7, 12, 8, 10, 15, 8, 13, 11, 10, 7, 11, 13, 14, 7, 10, 7, 8, 5, 9, 7, 2, 7, 9, 11, 3, 9, 7, 9, 14, 11, 11, 8, 13, 11, 8, 9, 12, 6, 8, 8, 13, 8, 11, 6, 6, 10, 7, 9, 6, 12, 14, 9, 5, 8, 11, 17, 12, 7, 4, 12, 11, 8, 10, 10, 8, 10, 15, 7, 9, 5, 12, 12, 10, 10, 7, 8, 96649824, 11, 6, 8, 10, 9, 12, 10, 7, 12, 14, 8, 6, 7, 4, 15, 10, 9, 6, 11, 11, 7, 13, 11, 14, 8, 12, 14, 11, 8, 8, 10, 8, 13, 12, 7, 14, 11, 14, 12, 15, 10, 8, 9, 12, 6, 289117, 9, 12, 11, 10, 5, 3639656, 7, 12, 13, 9, 11, 9, 15, 13, 10, 12, 7, 13, 8, 11, 12, 9, 9, 9, 5, 8, 10, 13, 8, 10, 7, 10, 10, 9, 11, 9, 13, 10, 13, 7, 8, 7, 8, 8, 6, 9, 9, 11, 6, 11, 12, 7, 9, 8, 9, 11, 10, 6, 9, 10, 11, 13, 7, 9, 9, 10, 13, 10, 3, 6, 13, 8, 11, 7, 9, 10, 12, 14, 8, 8, 7, 5, 12, 9, 8, 13, 10, 10, 9, 7, 5, 9, 12, 15, 10, 11, 14, 7, 6, 13, 9, 6, 10, 11, 11, 8, 14, 10, 6, 6, 8, 10, 10, 5, 8, 8, 11, 9, 9, 8, 12, 7, 5, 6, 8, 6, 7, 9, 9, 12, 9, 11, 8, 10, 3, 9, 10, 8, 10, 14, 12, 5, 11, 7, 6, 9, 10, 7, 8, 12, 7, 6, 8, 10, 12, 7, 8, 9, 9, 7, 9, 11, 11, 7, 7550340, 4, 10, 9, 11, 13, 10, 14, 7, 5, 15, 5, 12, 11, 13, 9, 12, 17783339, 11, 13, 14, 7, 9, 7, 10, 9, 10, 10, 12, 13, 10, 12, 9, 10, 9, 10, 9, 7, 12, 10, 8, 6, 9, 10, 9, 9, 12, 10, 11, 16, 5, 9, 12, 6, 12, 7, 10, 10, 10, 10, 14, 9, 14, 7, 11, 9, 6, 16, 8, 17, 11, 8, 11, 6, 7, 15, 9, 9, 9, 10, 4, 12, 6, 6, 4, 8, 10, 7, 9, 15, 9, 14, 13, 10, 15, 9, 5, 10, 8, 10, 12, 9, 10, 9, 8, 13, 7, 11, 11, 11, 10, 10, 12, 9, 12, 11, 13, 10, 15, 12, 15, 7, 7, 13, 14, 14, 5, 9, 7, 3, 14, 10, 6, 10, 10, 6, 15, 11, 5, 9, 9, 8, 14, 11, 10, 11, 11, 15, 5, 9, 8, 9, 12, 12, 15, 15, 8, 7, 14, 6, 11, 11, 7, 10, 15, 7, 15, 6, 8, 8, 16, 9, 12, 9, 8, 4, 6, 15, 10, 9, 5, 7, 8, 4, 9, 7, 8, 10, 14, 14, 5, 11, 9, 11, 8, 7, 11, 7, 11, 12, 8, 7, 7, 10, 9, 8, 10, 7, 9, 10, 11, 6, 9, 11, 9, 10, 12, 5, 14, 10, 11, 15, 7, 8, 12, 7, 9, 6, 6, 9, 8, 6, 9, 12, 12, 14, 6, 9, 14, 7, 5, 11, 14, 13, 8, 6, 9, 14, 10, 12, 6, 11, 11, 13, 9, 9, 10, 13, 9, 10, 7, 14, 4, 6, 10, 9, 8, 11, 14, 13, 6, 15, 6, 10, 11, 7, 6, 12, 10, 8, 13, 9, 10, 16, 11, 9, 13, 10, 10, 9, 9, 8, 12, 9, 6, 11, 10, 12, 16, 13, 6, 11, 10, 6, 9, 10, 7, 6, 10, 10, 12, 7, 8, 7, 11, 11, 15, 13, 11, 4, 9, 14, 11, 9, 9, 10, 14, 13, 8, 4536708, 12, 9, 4, 4, 7, 14, 8, 12, 7, 5957, 11, 7, 12, 9, 10, 12, 10, 11, 5, 6, 12, 9, 12, 12, 10, 4, 11, 10, 10, 7, 14, 7, 9, 9, 13, 8, 11, 5, 8, 11, 11, 7, 8, 9, 10, 13, 12, 10, 12, 9, 15, 11, 7, 10, 10, 9, 10, 10, 7, 14, 12, 6, 12, 7, 8, 14, 8, 11, 9, 10, 10, 12, 10, 9, 12, 10, 12, 14, 10, 9, 7, 9, 11, 10, 10, 12, 13, 8, 14, 13, 14, 10, 12, 9, 14, 13, 13, 14, 10, 10, 8, 15, 6, 7, 7, 7, 10, 8, 6, 5, 8, 10, 6, 12, 13, 10, 11, 10, 12, 7, 10, 12, 7, 5, 10, 6, 5, 12, 12, 10, 12, 9, 9, 10, 10, 13, 11, 8, 14, 11, 12, 9, 7, 9, 5, 12, 12, 4, 11, 6, 13, 9, 6, 11, 6, 4, 9, 10, 12, 8, 8, 12, 13, 14, 13, 9, 6, 10, 9, 14, 7, 4, 14, 10, 10, 9, 10, 10, 7, 11, 13, 8, 10, 13, 11, 5, 15, 7, 10, 9, 9, 3, 15, 9, 11, 7, 14, 10, 13, 12, 10, 13, 10, 15, 9, 14, 10, 10, 12, 10, 9, 8, 10, 6, 12, 12, 10, 5, 6, 8, 14, 10, 11, 14, 12, 10, 13, 9, 9, 10, 13}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 5, 11, 10, 7, 10, 4, 7, 6, 9, 7, 6, 8, 9, 10, 10, 14, 10, 12, 10, 8, 11, 9, 5, 8, 9, 9, 11, 9, 7, 12, 8, 3, 11, 5, 10, 11, 9, 16, 9, 5, 7, 12, 11, 9, 6, 10, 11, 10, 9, 9, 9, 5, 9, 12, 13, 6, 6, 10, 8, 9, 9, 5, 11, 8, 10, 5, 13, 9, 9, 11, 14, 11, 5, 9, 11, 14, 9, 9, 9, 11, 5, 6, 9, 11, 13, 12, 5, 11, 10, 9, 7, 9, 8, 9, 11, 10, 4, 9, 10, 9, 9, 10, 9, 9, 13, 10, 5, 8, 6, 14, 8, 9, 7, 6, 13, 12, 8, 10, 10, 11, 9, 5, 8, 5, 12, 9, 7, 10, 11, 8, 9, 9, 11, 10, 10, 9, 12, 5, 12, 8, 8, 4, 11, 5, 167258001, 10, 11, 12, 5, 10, 7, 10, 8, 11, 8, 8, 8, 12, 10, 9, 8, 12, 10, 10, 10, 4, 14, 10, 10, 11, 8, 10, 14, 11, 9, 9, 11, 11, 6, 6, 15, 5, 7, 3, 11, 6, 7, 16, 10, 10, 7, 9, 8, 8, 15, 8, 5, 15, 14, 13, 9, 12, 10, 9, 9, 7, 7, 10, 8, 12, 7, 12, 8, 11, 10, 10, 9, 9, 9, 8, 12, 7, 10, 11, 14, 11, 8, 11, 14, 10, 12, 11, 14, 8, 14, 6, 11, 8, 10, 7, 6, 9, 5, 9, 15, 13, 7, 14, 9, 11, 11, 11, 7, 11, 10, 13, 12, 7, 9, 9, 5, 8, 6, 6, 7, 10, 8, 8, 10, 11, 5, 10, 9, 7, 14, 8, 9, 10, 7, 11, 5, 9, 12, 11, 13, 10, 11, 9, 12, 10, 5, 5, 10, 10, 8, 4, 9, 5, 5, 9, 11, 10, 9, 11, 4, 10, 14, 10, 10, 8, 12, 6, 10, 6, 7, 11, 8, 10, 7, 10, 9, 11, 9, 11, 11, 13, 11, 9, 5, 14, 11, 11, 12, 9, 7, 12, 12, 9, 13, 12, 9, 11, 11, 10, 7, 8, 13, 7, 7, 6, 9, 11, 8, 11, 10, 12, 11, 12, 5, 7, 14, 11, 10, 10, 12, 4, 13, 10, 11, 10, 12, 9, 8, 16, 7, 6, 10, 8, 5, 15, 9, 9, 8, 8, 5, 12, 11, 9, 11, 6, 6, 11, 10, 16, 10, 13, 9, 12, 12, 11, 6, 10, 3, 8, 15, 12, 7, 11, 8, 10, 10, 10, 7, 15, 9, 8, 10, 7, 8, 14, 9, 9, 8, 9, 6, 9, 8, 13, 11, 7, 5, 6, 12, 6, 10, 12, 10, 11, 14, 13, 5, 10, 9, 9, 10, 10, 8, 6, 8, 6, 10, 13, 9, 11, 9, 10, 9, 11, 10, 10, 6, 9, 6, 10, 14, 7, 9, 8, 10, 12, 11, 8, 8, 11, 9, 8, 11, 15, 7, 11, 15, 13, 7, 10, 9, 7, 10, 7, 7, 9, 11, 6, 6, 10, 8, 14, 10, 7, 12, 12, 10, 10, 10, 9, 8, 7, 8, 9, 13, 6, 10, 8, 5, 9, 9, 10, 12, 6, 5, 7, 9, 9, 7, 12, 7, 9, 9, 5, 2, 12, 11, 11, 10, 12, 14, 8, 9, 6, 9, 10, 9, 12, 10, 10, 9, 11, 9, 16, 11, 12, 8, 9, 11, 9, 8, 11, 11, 10, 6, 9, 10, 9, 8, 7, 11, 14, 10, 11, 4, 10, 10, 9, 10, 7, 8, 10, 14, 12, 8, 10, 9, 6, 11, 10, 14, 2, 7, 7, 11, 11, 10, 13, 8, 13, 7, 8, 13, 9, 13, 9, 9, 10, 10, 13, 8, 5, 7, 11, 6, 7, 13, 9, 9, 8, 12, 7, 9, 8, 6, 11, 10, 8, 11, 10, 11, 8, 8, 11, 7, 13, 10, 9, 9, 9, 13, 7, 7, 12, 7, 5, 5, 10, 7, 10, 10, 11, 13, 10, 13, 10, 7, 9, 10, 7, 11, 8, 11, 9, 4, 8, 9, 11, 10, 9, 9, 8, 9, 10, 8, 8, 5, 8, 10, 8, 6, 14, 8, 6, 8, 9, 8, 10, 7, 10, 9, 6, 6, 8, 10, 4, 14, 11, 7, 11, 8, 7, 9, 9, 11, 11, 8, 7, 9, 15, 9, 8, 9, 14, 7, 6, 10, 10, 10, 9, 8, 11, 14, 11, 11, 14, 10, 5, 9, 8, 8, 9, 6, 11, 6, 4, 9, 10, 13, 6, 12, 7, 5, 8, 9, 6, 8, 11, 11, 5, 10, 14, 8, 10, 8, 12, 13, 8, 8, 12, 13, 10, 7, 8, 9, 11, 10, 8, 12, 10, 11, 10, 15, 12, 11, 9, 9, 5, 7, 7, 8, 7, 7, 8, 8, 9, 10, 9, 11, 16, 12, 11, 13, 11, 7, 11, 13, 11, 9, 9, 5, 12, 8, 11, 8, 7, 15, 8, 7, 11, 12, 7, 8, 13, 9, 12, 9, 10, 14, 11, 4, 14, 6, 5, 5, 11, 9, 12, 9, 7, 11, 14, 12, 5, 11, 10, 12, 12, 6, 10, 6, 5, 6, 11, 9, 8, 11, 11, 8, 15, 6, 7, 13, 9, 11, 10, 12, 12, 9, 10, 12, 7, 12, 11, 9, 5, 10, 9, 8, 6, 11, 9, 13, 13, 9, 13, 6, 8, 13, 12, 11, 12, 8, 10, 6, 8, 11, 9, 10, 12, 10, 6, 5, 8, 9, 8, 9, 8, 7, 12, 13, 3, 6, 5, 4, 4, 8, 5, 11, 7, 14, 10, 13, 9, 9, 12, 9, 7, 10, 11, 10, 10, 10, 9, 7, 8, 11, 9, 7, 8, 10, 8, 6, 9, 7, 9, 9, 6, 11, 12, 9, 9, 11, 10, 6, 13, 3, 10, 9, 13, 13, 4, 6, 7, 9, 12, 11, 8, 9, 7, 10, 7, 11, 10, 13, 11, 7, 11, 12, 9, 9, 9, 9, 11, 10, 9, 10, 10, 14, 9, 8, 14, 5, 4, 7, 8, 10, 5, 4, 10, 7, 6, 6, 6, 12, 14, 10, 11, 8, 9, 8}

Returns: {2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 5, 10, 8, 7, 12, 10, 12, 9, 8, 7, 13, 9, 10, 6, 10, 7, 10, 9, 9, 8, 8, 9, 11, 7, 7, 13, 11, 5, 10, 7, 12, 9, 8, 9, 4, 9, 5, 4, 8, 5, 10, 8, 7, 9, 12, 9, 13, 5, 7, 7, 6, 9, 12, 7, 6, 13, 8, 6, 6, 7, 7, 12, 4, 6, 10, 10, 5, 7, 7, 13, 9, 6, 5, 9, 7, 7, 11, 11, 10, 13, 6, 12, 10, 10, 13, 8, 9, 8, 9, 9, 13, 6, 8, 13, 7, 7, 7, 10, 8, 7, 12, 9, 7, 10, 7, 10, 4, 9, 13, 12, 10, 9, 7, 12, 9, 5, 7, 10, 9, 10, 13, 10, 10, 8, 10, 11, 9, 12, 6, 11, 5, 10, 7, 10, 9, 6, 6, 10, 8, 10, 11, 8, 7, 13, 7, 7, 6, 10, 6, 13, 7, 6, 10, 11, 10, 11, 9, 8, 7, 12, 7, 8, 6, 10, 7, 9, 11, 8, 6, 6, 8, 10, 9, 12, 7, 7, 5, 12, 10, 7, 7, 10, 12, 8, 7, 9, 10, 11, 4, 9, 6, 10, 6, 8, 10, 11, 7, 13, 9, 11, 8, 7, 9, 8, 9, 9, 6, 11, 7, 13, 4, 7, 9, 11, 9, 9, 9, 7, 13, 13, 10, 14, 15, 11, 4, 8, 11, 14, 10, 5, 8, 11, 14, 6, 10, 10, 7, 4, 9, 9, 11, 11, 11, 6, 9, 11, 6, 8, 10, 11, 13, 7, 9, 6, 10, 5, 11, 13, 12, 10, 7, 8, 6, 12, 9, 8, 11, 7, 7, 13, 12, 9, 10, 7, 10, 11, 6, 10, 9, 11, 10, 9, 4, 13, 7, 12, 5, 9, 6, 7, 11, 6, 6, 6, 12, 9, 11, 10, 6, 11, 8, 6, 4, 8, 4, 10, 10, 8, 5, 7, 7, 9, 9, 7, 7, 12, 9, 13, 11, 7, 8, 13, 13, 7, 8, 7, 9, 10, 7, 9, 9, 8, 7, 9, 8, 8, 11, 10, 9, 12, 10, 8, 7, 8, 10, 8, 9, 10, 6, 11, 7, 13, 8, 9, 10, 6, 9, 10, 8, 7, 11, 10, 7, 7, 11, 10, 5, 8, 7, 8, 4, 8, 9, 7, 4, 5, 11, 11, 15, 13, 10, 11, 9, 6, 9, 9, 7, 7, 7, 8, 8, 13, 4, 6, 9, 10, 8, 15, 9, 9, 10, 7, 8, 4, 6, 9, 9, 7, 8, 11, 7, 6, 7, 10, 11, 6, 8, 12, 4, 12, 7, 7, 7, 7, 13, 4, 10, 5, 8, 14, 7, 13, 6, 9, 7, 8, 11, 7, 11, 7, 7, 7, 11, 9, 12, 11, 10, 10, 9, 5, 6, 6, 9, 8, 4, 9, 11, 11, 7, 5, 13, 11, 10, 7, 8, 6, 13, 7, 10, 9, 7, 7, 8, 7, 8, 7, 8, 8, 8, 6, 7, 8, 8, 10, 9, 11, 11, 9, 7, 10, 9, 12, 8, 8, 6, 8, 8, 9, 6, 10, 9, 8, 8, 11, 10, 10, 7, 4, 8, 10, 10, 15, 9, 9, 10, 11, 10, 8, 13, 11, 11, 7, 12, 8, 8, 5, 9, 11, 9, 11, 11, 8, 9, 7, 10, 7, 7, 15, 10, 10, 7, 5, 13, 9, 8, 6, 11, 10, 9, 12, 7, 6, 10, 5, 6, 6, 14, 6, 9, 11, 9, 7, 10, 6, 4, 11, 11, 6, 10, 7, 8, 13, 9, 9, 8, 7, 11, 9, 9, 12, 8, 10, 6, 11, 12, 9, 8, 7, 8, 10, 7, 13, 8, 4, 7, 11, 9, 7, 5, 10, 11, 9, 7, 5, 10, 8, 10, 7, 7, 12, 5, 9, 4, 8, 9, 10, 6, 7, 7, 12, 8, 10, 6, 6, 9, 10, 12, 9, 7, 10, 9, 10, 7, 7, 13, 11, 8, 7, 13, 8, 10, 12, 8, 7, 14, 14, 5, 9, 5, 10, 8, 8, 7, 10, 5, 5, 6, 9, 12, 11, 9, 10, 9, 9, 10, 8, 9, 8, 6, 12, 10, 7, 6, 10, 4, 9, 9, 6, 10, 8, 13, 8, 7, 7, 9, 9, 11, 10, 2, 9, 11, 11, 8, 6, 4, 9, 10, 14, 12, 13, 8, 6, 8, 11, 7, 14, 11, 8, 10, 7, 5, 4, 13, 9, 9, 10, 10, 8, 9, 7, 13, 9, 9, 8, 6, 10, 7, 9, 10, 10, 9, 11, 6, 8, 9, 9, 7, 5, 10, 13, 7, 12, 8, 29231779, 9, 12, 8, 6, 10, 7, 6, 8, 6, 11, 8, 7, 9, 6, 10, 8, 9, 10, 9, 9, 10, 8, 9, 8, 10, 8, 10, 8, 6, 11, 8, 9, 8, 9, 9, 5, 11, 10, 11, 10, 7, 8, 9, 8, 9, 6, 7, 6, 6, 7, 11, 9, 8, 11, 9, 4, 5, 7, 5, 14, 10, 8, 13, 7, 12, 12, 10, 5, 10, 9, 10, 14, 8, 11, 7, 9, 10, 8, 9, 8, 5, 12, 7, 11, 13, 7, 4, 7, 8, 10, 6, 9, 3, 9, 4, 12, 7, 12, 7, 9, 8, 9, 9, 11, 8, 10, 7, 10, 9, 9, 8, 10, 6, 9, 12, 10, 15, 10, 7, 14, 8, 6, 7, 8, 9, 7, 10, 11, 13, 13, 10, 11, 10, 9, 10, 8, 7, 7, 12, 9, 6, 8, 6, 11, 10, 4, 8, 10, 9, 14, 6, 8, 10, 5, 11, 10, 9, 13, 6, 8, 11, 9, 12, 8, 9, 10, 9, 12, 8, 4, 6, 26238109, 4, 9, 8, 7, 10, 4, 11, 8, 8, 6, 10, 8, 8, 6, 9, 9, 6, 5, 8, 8, 11, 10, 7, 8, 10, 10, 7, 10, 7, 13, 11, 8, 8, 4, 9, 8, 10, 6, 9, 10, 7, 6, 9, 13, 5, 10, 7, 11, 10, 9, 6, 8, 11, 5, 10, 8, 10, 10, 12, 6, 11, 7, 12, 10, 5, 10, 10, 7, 8, 10, 10, 10, 3, 10, 10, 11, 4, 12, 7, 9, 11, 8}

Returns: {-1 }
{10, 8, 7, 10, 9, 7, 7, 9, 7, 9, 9, 12, 6, 7, 10, 7, 7, 6, 7, 6, 8, 6, 7, 7, 7, 5, 7, 7, 8, 8, 8, 6, 11, 10, 8, 6, 8, 8, 8, 8, 10, 9, 5, 5, 11, 5, 7, 7, 9, 6, 10, 10, 5, 7, 12, 8, 6, 10, 6, 7, 8, 8, 6, 9, 3, 7, 11, 6, 9, 9, 10, 8, 8, 6, 9, 6, 9, 11, 9, 10, 8, 7, 6, 7, 9, 6, 8, 9, 8, 8, 7, 6, 4, 9, 7, 7, 8, 7, 8, 6, 9, 8, 12, 8, 11, 10, 6, 8, 7, 6, 10, 6, 9, 6, 9, 9, 7, 7, 5, 7, 7, 9, 11, 9, 6, 8, 8, 9, 12, 8, 6, 9, 8, 5, 8, 7, 10, 10, 9, 11, 10, 9, 116036521, 11, 10, 9, 12, 5, 9, 7, 6, 9, 9, 9, 10, 12, 12, 8, 9, 8, 5, 8, 9, 11, 8, 6, 7, 7, 8, 11, 8, 9, 11, 8, 7, 13, 11, 9, 11, 9, 7, 6, 5, 5, 6, 6, 166962, 8, 8, 9, 9, 9, 11, 11, 9, 514480333, 7, 10, 6, 5, 6, 9, 8, 8, 5, 8, 8, 9, 9, 6, 6, 9, 7, 7, 5, 6, 7, 6, 9, 8, 7, 11, 5, 9, 9, 6, 8, 9, 3505409, 3, 10, 10, 9, 10, 8, 6, 6, 9, 6, 5, 7, 8, 11, 7, 7, 9, 9, 7, 7, 10, 9, 5, 9, 10, 9, 7, 10, 9, 10, 10, 8, 8, 8, 7, 10, 11, 6, 9, 10, 8, 6, 6, 6, 6, 9, 8, 6, 9, 10, 6, 7, 9, 7, 8, 8, 7, 9, 9, 10, 12, 10, 7, 10, 8, 7, 10, 9, 7, 8, 7, 8, 7, 9, 11, 6, 6, 6, 6, 6, 8, 8, 7, 7, 10, 7, 10, 10, 4, 7, 7, 7, 9, 8, 7, 10, 9, 9, 10, 10, 9, 11, 6, 9, 9, 7, 11, 6, 11, 9, 9, 7, 6, 8, 10, 9, 6, 11, 5, 7, 9, 11, 12, 10, 13, 9, 6, 6, 11, 9, 7, 8, 6, 10, 6, 9, 8, 9, 10, 11, 6, 9, 11, 2, 8, 8, 7, 7, 7, 11, 9, 12, 5, 9, 7, 8, 8, 6, 7, 7, 9, 6, 5, 6, 12, 11, 7, 5, 12, 8, 9, 11, 7, 8, 7, 6, 8, 9, 7, 10, 8, 8, 9, 8, 6, 12, 5, 5, 8, 8, 8, 10, 6, 8, 8, 8, 8, 8, 9, 9, 8, 5, 10, 8, 10, 6, 11, 8, 10, 7, 12, 8, 8, 8, 12, 8, 8, 8, 10, 11, 7, 8, 7, 6, 9, 11, 10, 10, 9, 11, 5, 7, 7, 8, 9, 7, 8, 9, 8, 11, 8, 8, 12, 6, 8, 9, 8, 10, 10, 6, 9, 11, 5, 7, 7, 6, 6, 7, 10, 5, 8, 9, 10, 9, 7, 8, 6, 11, 10, 8, 9, 11, 10, 4, 8, 9, 10, 7, 9, 7, 8, 5, 9, 4, 11, 8, 7, 9, 9, 10, 7, 9, 8, 7, 35214882, 7, 6, 8, 6, 6, 10, 9, 7, 10, 7, 6, 8, 9, 6, 11, 9, 5, 5, 6, 6, 4, 9, 9, 9, 10, 5, 5, 9, 9, 6, 11, 11, 7, 7, 11, 7, 9, 9, 8, 8, 10, 7, 8, 6, 7, 8, 11, 7, 5, 7, 6, 6, 10, 10, 7, 7, 7, 7, 12, 11, 8, 9, 5, 6, 8, 9, 6, 10, 7, 8, 10, 6, 8, 6, 8, 10, 11, 7, 9, 8, 11, 7, 9, 9, 9, 8, 7, 9, 10, 9, 9, 8, 7, 7, 10, 4, 9, 5, 8, 7, 11, 4, 11, 7, 9, 7, 9, 9, 7, 7, 5, 9, 7, 12, 4, 12, 10, 9, 12, 10, 9, 9, 9, 7, 5, 10, 7, 11, 3387, 11, 5, 8, 8, 7, 5, 10, 8, 7, 9, 9, 8, 9, 10, 9, 8, 8, 5, 9, 8, 7, 9, 6, 4, 6, 7, 11, 8, 7, 9, 7, 7, 8, 8, 12, 10, 6, 5, 6, 7, 9, 7, 3, 11, 12, 7, 10, 10, 5, 5, 10, 13, 8, 8, 6, 5, 9, 10, 9, 9, 7, 8, 7, 7, 9, 9, 11, 3, 9, 9, 8, 7, 9, 7, 9, 10, 8, 7, 5, 8, 10, 5, 8, 8, 8, 7, 7, 7, 11, 10, 9, 10, 9, 8, 9, 8, 6904509, 4, 3, 6, 6, 12, 6, 8, 6, 10, 7, 11, 8, 9, 4, 10, 9, 9, 11, 8, 7, 7, 8, 7, 10, 7, 5, 5, 9, 7, 8, 6, 7, 7, 9, 7, 8, 8, 7, 8, 12, 11, 7, 7, 11, 9, 8, 7, 7, 8, 8, 9, 9, 12, 10, 9, 3, 10, 9, 8, 9, 9, 7, 11, 11, 8, 7, 8, 6, 9, 12, 6, 7, 10, 7, 10, 9, 9, 9, 12, 12, 9, 6, 8, 9, 9, 9, 9, 6, 11, 9, 9, 9, 8, 10, 8, 8, 6, 10, 12, 12, 9, 7, 9, 8, 7, 12, 9, 10, 10, 8, 8, 10, 987031, 8, 10, 10, 8, 6, 6, 8, 10, 7, 6, 10, 5, 6, 5, 7, 10, 8, 9, 7, 10, 12, 5, 10, 12, 7, 6, 11, 11, 9, 10, 3, 7, 7, 9, 6, 8, 8, 8, 8, 9, 9, 7, 10, 11, 12, 9, 6, 8, 9, 7, 8, 11, 7, 6, 9, 6, 6, 11, 11, 9, 7, 7, 7, 6, 9, 11, 7, 6, 7, 5, 10, 12, 8, 10, 9, 9, 8, 9, 8, 9, 11, 10, 9, 9, 7, 9, 9, 9, 8, 6, 10, 9, 7, 7, 9, 10, 9, 10, 8, 11, 8, 6, 9, 10, 7, 8, 7, 10, 11, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{9, 17, 8, 7, 13, 16, 8, 12, 16, 3, 8, 10, 13, 12, 13, 8, 10, 8, 13, 7, 10, 9, 15, 14, 12, 7, 8, 14, 17, 6, 14, 9, 11, 14, 15, 14, 11, 15, 12, 11, 16, 3, 11, 9, 10, 10, 2, 15, 7, 8, 10, 13, 9, 8, 13, 9, 11, 5, 8, 8, 13, 14, 9, 15, 5, 9, 16, 8, 10, 17, 9, 4, 8, 15, 10, 7, 16, 9, 8, 7, 11, 17, 13, 16, 10, 9, 5, 8, 13, 9, 4, 10, 9, 11, 8, 8, 10, 16, 7, 13, 6, 10, 11, 7, 10, 9, 15, 21, 8, 8, 8, 8, 7, 10, 7, 9, 9, 20, 8, 10, 11, 9, 8, 11, 8, 10, 14, 11, 10, 8, 13, 8, 10, 13, 13, 7, 18, 12, 17, 7, 13, 8, 11, 12, 7, 12, 8, 9, 10, 11, 10, 5, 7, 6, 8, 8, 11, 14, 9, 8, 6, 8, 10, 6, 17, 9, 8, 6, 14, 18, 9, 3012, 15, 12, 6, 12, 10, 7, 11, 7, 13, 13, 10, 13, 14, 12, 14, 11, 9, 8, 11, 12, 12, 10, 11, 8, 16, 9, 9, 8, 10, 8, 15, 11, 13, 5, 7, 15, 8, 8, 7, 13, 8, 9, 10, 6, 7, 7, 14, 11, 11, 8, 7, 6, 7, 9, 12, 5, 8, 8, 10, 6, 12, 15, 13, 21, 7, 11, 8, 13, 10, 4, 9, 11, 7, 12, 18, 10, 9, 8, 8, 8, 3, 10, 8, 14, 16, 6, 9, 11, 10, 11, 14, 16, 15, 10, 9, 9, 10, 12, 11, 8, 9, 7, 10, 11, 12, 10, 11, 16, 6, 10, 9, 9, 16, 8, 17, 12, 8, 13, 8, 9, 19, 8, 11, 10, 12, 15, 13, 17, 15, 7, 10, 8, 8, 12, 5, 9, 15, 10, 7, 13, 9, 9, 13, 8, 10, 10, 2, 9, 8, 8, 10, 13, 8, 11, 12, 7, 11, 18, 8, 13, 10, 14, 8, 6, 10, 13, 10, 10, 11, 9, 4, 12, 12, 10, 9, 10, 16, 8, 9, 12, 9, 17, 10, 9, 8, 6, 9, 10, 7, 12, 12, 19, 9, 12, 7, 10, 6, 9, 12, 8, 11, 10, 10, 12, 10, 8, 6, 13, 9, 12, 14, 12, 9, 9, 10, 9, 8, 10, 10, 17, 6, 8, 16, 8, 12, 14, 7, 15, 9, 9, 7, 8, 14, 16, 8, 15, 8, 16, 9, 9, 7, 9, 16, 9, 8, 6, 9, 6, 12, 17, 7, 16, 1, 11, 10, 15, 10, 4, 11, 6, 11, 13, 10, 10, 13, 13, 6, 17, 12, 9, 11, 9, 7, 9, 9, 12, 14, 7, 14, 8, 6, 15, 14, 11, 13, 9, 11, 6, 8, 9, 6, 10, 8, 15, 15, 8, 10, 8, 9, 9, 9, 11, 9, 15, 16, 7, 6, 12, 11, 6, 7, 8, 6, 6, 10, 6, 14, 18, 9, 4, 6, 8, 10, 7, 14, 7, 15, 9, 12, 16, 8, 15, 15, 8, 11, 9, 14, 14, 10, 16, 15, 8, 15, 13, 9, 15, 11, 15, 14, 8, 7, 14, 16, 11, 10, 9, 10, 10, 17, 11, 13, 7, 18, 8, 10, 10, 8, 8, 14, 15, 13, 7, 10, 7, 13, 14, 9, 10, 16, 10, 10, 8, 13, 10, 10, 8, 10, 14, 14, 11, 1442616, 16, 8, 10, 8, 10, 9, 8, 14, 10, 10, 7, 9, 14, 8, 13, 12, 13, 8, 10, 10, 8, 9, 15, 7, 6, 10, 5, 16, 16, 9, 242529227, 6, 8, 6, 10, 10, 9, 6, 10, 10, 15, 14, 13, 9, 9, 12, 14, 8, 14, 12, 11, 6, 16, 15, 14, 19, 14, 10, 6, 10, 11, 10, 12, 8, 7, 14, 14, 7, 17, 13, 7, 7, 10, 13, 14, 13, 15, 8, 14, 7, 17, 14, 10, 16, 12, 9, 11, 7, 15, 7, 10, 8, 14, 12, 15, 12, 10, 13, 10, 15, 8, 15, 9, 13, 11, 10, 12, 8, 16, 9, 7, 15, 9, 13, 12, 11, 10, 13, 14, 15, 17, 12, 12, 14, 19, 10, 8, 15, 14, 14, 8, 11, 7, 9, 7, 12, 7, 9, 9, 8, 7, 7, 12, 5, 9, 17, 11, 8, 8, 16, 11, 12, 9, 11, 6, 14, 7, 8, 8, 7, 14, 14, 8, 11, 9, 8, 15, 8, 8, 10, 17, 7, 7, 10, 9, 12, 7, 11, 14, 13, 5, 15, 12, 8, 8, 13, 10, 6, 10, 9, 7, 13, 11, 10, 14, 19, 7, 16, 10, 9, 14, 9, 12, 7, 8, 6, 14, 8, 12, 18, 16, 14, 10, 7, 8, 89778593, 17, 13, 15, 12, 8, 8, 8, 9, 8, 14, 8, 13, 13, 11, 6, 9, 10, 13, 14, 9, 14, 13, 8, 8, 18, 14, 9, 6, 13, 13, 9, 7, 3, 10, 5, 8, 9, 10, 12, 13, 12, 11, 10, 15, 10, 15, 14, 18, 5, 17, 18, 6, 20, 7, 14, 18, 13, 7, 8, 14, 14, 4, 14, 9, 6, 16, 8, 12, 8, 12, 12, 9, 14, 9, 13, 8, 10, 8, 10, 12, 13, 10, 14, 9, 14, 8, 11, 7, 11, 14, 14, 4, 16, 13, 15, 9, 10, 6, 13, 13, 10, 6, 8, 23942, 8, 15, 7, 15, 8, 13, 7, 11, 15, 10, 16, 8, 12, 10, 15, 10, 8, 10, 13, 7, 10, 9, 6, 14, 10, 8, 14, 21, 16, 13, 15, 9, 10, 12, 17, 16, 10, 12, 6, 5, 15, 13, 4, 10, 8, 9, 11, 11, 9, 8, 8, 14, 10, 10, 9, 8, 10, 11, 8, 16, 10, 12, 12, 7, 10, 10, 7, 8, 10, 7, 16, 13, 6, 17, 11, 11, 12, 9, 10}

Returns: {-1 }
{6, 9, 9, 13, 11, 8, 6, 7, 12, 4, 6, 6, 9, 6, 8, 8, 12, 8, 9, 7, 7, 8, 10, 9, 8, 11, 11, 10, 6, 12, 15, 101716, 12, 6, 8, 5, 9, 6, 8, 9, 7, 11, 7, 7, 11, 7, 5, 3, 10, 8, 8, 8, 7, 5, 11, 9, 8, 13, 8, 11, 10, 6, 12, 14, 10, 8, 11, 6, 13, 6, 7, 7, 12, 7, 8, 10, 9, 6, 8, 9, 11, 7, 6, 10, 12, 10, 9, 9, 8, 7, 12, 11, 10, 6, 14, 6, 6, 14, 12, 10, 7, 8, 13, 5, 10, 11, 10, 10, 10, 8, 8, 12, 10, 8, 7, 107368, 10, 16, 9, 4, 12, 8, 9, 8, 12, 13, 11, 4, 10, 9, 7, 8, 7, 8, 5, 6, 7, 19642065, 9, 7, 9, 12, 5, 11, 7, 3514, 11, 6, 6, 6, 10, 10, 17, 7, 7, 10, 10, 9, 6, 12, 9, 7, 3, 7, 12, 10, 9, 6, 10, 8, 11, 8, 11, 16, 8, 7, 9, 12, 5, 7, 12, 9, 11, 11, 7, 11, 6, 4, 11, 6, 9, 9, 6, 7, 10, 2796095, 9, 5, 7, 13, 8, 8, 6, 8, 4, 11, 7, 11, 6, 11, 9, 9, 6, 11, 3595, 11, 15, 12, 7, 17, 7, 10, 10, 11, 12, 7, 10, 5, 17, 7, 15, 9, 8, 10, 6, 9, 6, 10, 7, 7, 10, 10, 8, 3, 8, 9, 7, 9, 7, 12, 8, 12, 7, 8, 7, 159006, 4, 5, 9, 7, 9, 6, 13, 7, 9, 5, 7, 8, 9, 6, 8, 7, 10, 9, 5, 9, 8, 6, 11, 10, 6, 6, 14, 5, 7, 7, 8, 12, 8, 6, 109272133, 9, 12, 9, 5, 10, 11, 6, 8, 11, 7, 10, 8, 7, 11, 9, 20164, 11, 11, 15, 9, 28161, 6, 9, 7, 6, 7, 6, 233121409, 10, 6, 7, 4, 12, 9, 10, 7, 6, 13, 14, 4, 6, 13, 7, 13, 5, 8, 7, 8, 12, 9, 13, 6, 7, 12, 7, 7, 5, 5, 7, 7, 9, 7, 10, 7, 12, 14, 10, 11, 10, 11, 14, 8, 9, 8, 10, 9, 9, 8, 14, 11, 8, 8, 9, 6, 13, 9, 12, 5, 5, 7, 13, 13, 7, 7, 7, 7, 11, 10, 13, 10, 7, 9, 9, 7, 5, 9, 10, 8, 12, 7, 12, 9, 13, 12, 6, 8, 12, 9, 8, 5, 10, 7, 6, 11, 17, 6, 7, 8521928, 12, 8, 7, 10, 11, 5, 10, 7, 13, 6, 7, 9, 1299049, 8, 12, 12, 9, 10, 8, 8, 11, 8, 7, 10, 7, 10, 8, 10, 13, 4, 118711214, 9, 4, 8, 8, 12, 9, 12, 9, 3, 6, 5, 13, 12, 11, 9, 11, 16, 9, 6, 7, 12, 7, 5, 7, 6, 7, 15, 10, 9, 12, 5, 5, 13, 12, 9, 7, 10, 3, 11, 11, 10, 10, 13, 8, 9, 10, 13, 6, 4, 9, 9, 11, 9, 7, 6, 12, 10, 6, 12, 9, 9, 11, 11, 6, 11, 8, 11, 7, 8, 9, 9, 11, 7, 12, 6, 11, 7, 10, 6, 7, 12, 11, 6, 8, 15, 14, 12, 8, 7, 9, 14, 9, 9, 9, 7, 3, 12, 12, 10, 10, 7, 11, 7, 9, 7, 8, 8, 16, 8, 14, 10, 7, 12, 10, 14, 8, 5, 8, 10, 6, 7, 7, 10, 11, 11, 17, 6, 14, 8, 10, 7, 10, 4, 7, 10, 16, 14, 6, 9, 8, 7, 9, 7, 5, 11, 6, 13, 10, 7, 7, 8, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 8, 4, 4, 6, 13, 6, 7, 7, 8, 9, 5, 9, 7, 12, 5, 6, 6, 8, 8, 9, 13, 6, 11, 10, 7, 8, 5, 8, 7, 7, 9, 13, 10, 5, 12, 8, 8, 8, 7, 12, 8, 6, 12, 13, 5, 10, 63551, 10, 12, 7, 7, 13, 10, 9, 8, 6, 8, 5, 10, 10, 8, 5, 14, 11, 11, 9, 9, 10, 7, 13, 10, 5, 7, 8, 6, 12, 6, 5, 13, 6, 8, 11, 10, 9, 10, 6, 9, 6, 7, 7, 11, 6, 10, 8, 11, 5, 5, 10, 7, 9, 9, 11, 6, 6, 5, 938122, 12, 7, 5, 10, 10, 8, 7, 8, 12, 6, 11, 8, 7, 4, 9, 6, 8, 6, 10, 13, 11, 12, 12, 13, 8, 10, 6, 8, 6, 8, 12, 9, 14, 6, 8, 8, 4, 12, 7, 6, 10, 7, 7, 9, 10, 6, 11, 12, 13, 9, 10, 5, 8, 7, 7, 6, 12, 10, 86694247, 16, 7, 7, 8679, 11, 8, 5, 8, 8, 7, 14, 12, 12, 6, 4, 7, 8, 6, 9, 12, 11, 10, 10, 7, 9, 5, 7, 8, 12, 9, 11, 9, 12, 16, 5, 10, 10, 9, 7, 5, 2199, 11, 8, 8, 6, 9, 6, 11, 6, 7, 7, 8, 10, 10, 7, 9, 7, 6, 9, 10, 13, 11, 10, 9, 9, 5, 13, 8, 9, 7, 11, 8, 7, 6, 8, 8, 7, 7, 12, 9, 13, 9, 11, 9, 12, 8, 8, 10, 7, 6, 6, 12, 12, 9, 9, 6, 17, 8, 7, 10, 7, 6077, 7, 6, 9, 10, 3, 10, 12, 10, 4, 8, 5, 7, 9, 10, 13, 8, 11, 7, 10, 8, 10, 12, 13, 9, 7, 10, 9, 14, 7, 7, 7, 5, 3, 11, 7, 7, 11, 12, 10, 12, 6, 10, 7, 7, 11, 14, 8, 9, 13, 5, 8, 7, 9, 13, 11, 5, 10, 4, 7, 11, 6, 14, 12, 9, 11, 9, 7, 10, 6, 9, 7, 13, 13, 7, 7, 10, 6, 10, 14, 11, 11, 13, 10, 7, 10, 7, 7, 9, 11, 6, 12, 11, 7, 8, 10, 13, 10, 7, 13, 11, 6, 7, 9, 13, 7, 8, 8, 8, 9, 7, 10, 9, 9, 6, 9, 8, 7}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{11, 6, 7, 6, 8, 9, 5, 9, 4, 7, 7, 10, 9, 8, 8, 8, 11, 7, 8, 11, 10, 9, 8, 9, 5, 8, 8, 10, 7, 8, 8, 7, 11, 6, 8, 9, 6, 8, 9, 8, 10, 10, 9, 8, 7, 8, 9, 7, 9, 11, 5, 4, 6, 5, 10, 11, 9, 11, 5, 8, 8, 6, 4, 11, 8, 10, 4, 7, 10, 13, 10, 8, 8, 10, 10, 9, 7, 10, 12, 8, 8, 7, 6, 6, 6, 10, 6, 9, 8, 8, 8, 7, 9, 9, 7, 9, 6, 8, 8, 6, 10, 9, 11, 7, 7, 8, 8, 10, 10, 7, 5, 9, 5, 10, 7, 9, 14, 8, 13, 8, 11, 10, 10, 9, 8, 7, 8, 9, 12, 4, 9, 12, 8, 10, 8, 10, 6, 8, 6, 8, 10, 8, 6, 7, 7, 12, 10, 9, 9, 9, 7, 8, 8, 5, 9, 10, 9, 7, 10, 11, 9, 5, 10, 7, 11, 11, 11, 7, 11, 5, 9, 11, 9, 8, 10, 9, 9, 8, 11, 9, 8, 12, 9, 8, 9, 9, 10, 10, 7, 5, 5, 9, 11, 10, 9, 8, 7, 9, 6, 8, 13, 9, 6, 9, 10, 13, 8, 7, 6, 10, 5, 8, 13, 8, 7, 7, 4, 10, 8, 9, 5, 9, 10, 7, 6, 8, 14, 7, 10, 12, 8, 8, 10, 10, 8, 8, 9, 9, 9, 8, 8, 6, 10, 8, 7, 12, 8, 11, 8, 11, 10, 8, 7, 8, 10, 8, 8, 8, 8, 8, 11, 6, 7, 9, 9, 9, 9, 9, 9, 9, 12, 10, 8, 8, 11, 7, 7, 10, 10, 10, 4520904, 14, 7, 8, 5, 6, 12, 11, 11, 6, 7, 6, 9, 10, 8, 6, 9, 6, 11, 8, 10, 9, 9, 6, 10, 6, 8, 10, 8, 7, 8, 5, 10, 3, 8, 9, 6, 8, 7, 10, 6, 10, 11, 11, 8, 8, 6, 7, 11, 9, 6, 10, 8, 8, 11, 9, 9, 9, 9, 9, 10, 9, 5, 7, 10, 9, 9, 8, 7, 4, 6, 9, 8, 9, 11, 10, 8, 8, 6, 5, 5, 9, 8, 8, 2, 8, 9, 8, 8, 10, 9, 7, 11, 9, 8, 7, 7, 8, 5, 5, 9, 8, 9, 9, 9, 9, 11, 7, 6, 7, 7, 10, 10, 11, 10, 5, 8, 10, 10, 9, 8, 8, 8, 11, 11, 8, 7, 10, 8, 9, 9, 9, 6, 12, 9, 8, 11, 12, 7, 11, 9, 8, 8, 10, 8, 8, 9, 15, 12, 8, 7, 14, 7, 7, 8, 8, 8, 7, 8, 10, 7, 9, 6, 12, 8, 13, 8, 9, 7, 7, 8, 8, 7, 10, 10, 10, 10, 7, 12, 11, 9, 9, 8, 7, 9, 7, 9, 4, 7, 9, 11, 6, 9, 4, 7, 8, 8, 9, 7, 10, 8, 4, 8, 8, 8, 6, 5, 7, 5, 11, 11, 9, 9, 8, 7, 10, 9, 8, 10, 14, 11, 9, 8, 7, 8, 10, 11, 8, 7, 8, 10, 9, 10, 7, 10, 7, 8, 4, 10, 9, 14, 5, 8, 6, 8, 9, 7, 9, 8, 7, 9, 9, 10, 8, 9, 10, 11, 10, 12, 8, 7, 8, 10, 7, 7, 5, 8, 5, 11, 6, 7, 8, 5507618, 9, 9, 9, 10, 9, 10, 8, 7, 7, 8, 5, 7, 10, 14, 11, 9, 6, 10, 2, 5, 8, 8, 7, 9, 9, 8, 8, 10, 9, 7, 12, 9, 7, 9, 8, 7, 6, 8, 8, 9, 10, 9, 7, 4, 9, 11, 11, 7, 8, 7, 9, 10, 5, 6, 8, 8, 8, 7, 8, 10, 7, 10, 10, 9, 5, 9, 8, 6, 8, 6, 8, 7, 10, 10, 6, 6, 9, 7, 11, 439611471, 7, 8, 8, 10, 10, 14, 7, 8, 8, 8, 11, 8, 4, 5, 7, 9, 6, 10, 10, 8, 11, 6, 11, 9, 7, 9, 15, 10, 7, 8, 5, 5, 8, 12, 8, 9, 4, 7, 6, 9, 7, 8, 11, 8, 9, 7, 7, 6, 8, 11, 8, 7, 10, 9, 7, 9, 9, 6, 10, 7, 10, 7, 8, 7, 10, 8, 11, 8, 8, 8, 8, 9, 7, 5, 10, 9, 9, 7, 7, 9, 6, 10, 6, 6, 11, 8, 8, 6, 10, 7, 9, 8, 10, 7, 7, 11, 10, 8, 7, 9, 9, 11, 12, 11, 11, 7, 9, 7, 7, 8, 8, 7, 11, 8, 8, 9, 10, 10, 6, 8, 13, 9, 9, 8, 9, 11, 8, 6, 11, 7, 9, 6, 7, 6, 9, 5, 9, 9, 10, 10, 12, 4138, 7, 6, 10, 9, 8, 10, 7, 6, 9, 8, 8, 8, 8, 9, 3, 8, 8, 10, 1639232, 5, 9, 5, 7, 8, 8, 8, 8, 7, 6, 8, 10, 11, 6, 6, 5, 8, 10, 8, 9, 11, 6, 8, 6, 8, 5, 8, 9, 12, 7, 10, 9, 11, 7, 4, 7, 9, 10, 7, 7, 12, 6, 11, 11, 8, 7, 6, 10, 10, 7, 7, 10, 9, 9, 8, 11, 6, 7, 8, 8, 9, 7, 7, 8, 10, 6, 7, 7, 8, 5, 8, 8, 9, 8, 5, 10, 11, 8, 9, 6, 5, 5, 6, 6, 6, 4, 11, 9, 9, 7, 9, 7, 5, 9, 8, 7, 8, 24337, 9, 6101869, 8, 14, 4, 9, 12, 10, 7, 6, 9, 6, 8, 9, 8, 6, 10, 8, 5, 8, 7, 9, 8, 6, 9, 10, 8, 9, 7, 8, 7, 8, 6, 10, 9, 9, 10, 9, 8, 4, 9, 6, 8, 11, 4, 15, 7, 8, 10, 8, 7, 11, 9, 13, 10, 9, 11, 8, 4, 11, 8, 8, 8, 10, 7, 14, 9, 8, 10, 6, 4, 14, 10, 10, 6, 7, 11, 11, 7, 9, 9, 4, 12, 8, 7, 9, 10, 5, 6, 7, 9, 9, 9, 11, 5, 7, 10, 10, 7, 10, 11, 10, 8, 6, 11, 11}

Returns: {2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 6, 11, 10, 10, 9, 12, 13, 10, 10, 5, 6, 7, 10, 13, 10, 7, 11, 9, 9, 10, 7, 9, 11, 12, 10, 7, 8, 4, 7, 8, 7, 15, 6, 7, 9, 7, 7, 7, 11, 12, 11, 9, 8, 7, 9, 12, 9, 12, 6, 9, 9, 8, 9, 7, 6, 8, 13, 7, 12, 9, 4, 8, 7, 13, 7, 11, 12, 8, 5, 7, 12, 5, 10, 11, 13, 10, 6, 12, 10, 12, 6, 11, 2, 12, 9, 10, 11, 8, 6, 12, 9, 8, 7, 10, 9, 10, 10, 13, 10, 5, 12, 8, 10, 9, 10, 11, 8, 14, 10, 10, 6, 10, 15, 11, 9, 10, 11, 10, 7, 6, 9, 8, 9, 7, 12, 10, 9, 10, 13, 8, 13, 11, 11, 12, 7, 13, 8, 11, 9, 9, 8, 11, 10, 9, 10, 5, 10, 7, 9, 10, 14, 7, 13, 9, 10, 9, 11, 12, 8, 9, 7, 6, 10, 13, 9, 9, 10, 10, 10, 8, 11, 10, 12, 4, 10, 7, 12, 11, 5, 13, 13, 4, 9, 13, 12, 4, 8, 9, 9, 10, 13, 13, 11, 4, 10, 8, 8, 8, 11, 11, 8, 6, 10, 6, 8, 12, 8, 6, 11, 13, 9, 8, 11, 10, 12, 9, 10, 11, 8, 8, 5, 6, 8, 9, 12, 14, 9, 6, 8, 14, 9, 6, 12, 4, 12, 7, 5, 12, 12, 9, 12, 5, 11, 6, 5, 10, 10, 9, 12, 12, 10, 8, 13, 8, 10, 10, 8, 11, 9, 7, 13, 12, 12, 12, 12, 8, 13, 6, 10, 12, 8, 12, 9, 13, 13, 7, 7, 12, 12, 7, 8, 12, 10, 8, 7, 10, 9, 10, 6, 11, 11, 10, 8, 11, 8, 9, 8, 6, 10, 13, 8, 3, 12, 7, 7, 7, 9, 12, 10, 9, 8, 8, 8, 12, 13, 5, 10, 5, 10, 8, 11, 8, 10, 9, 9, 13, 12, 10, 8, 14, 8, 10, 7, 10, 5, 8, 7, 7, 7, 9, 9, 12, 10, 7, 9, 11, 10, 11, 9, 7, 12, 7, 9, 7, 8, 11, 10, 11, 8, 8, 11, 10, 7, 9, 7, 12, 7, 9, 9, 6, 8, 6, 12, 13, 7, 12, 10, 6, 9, 8, 7, 12, 4, 8, 11, 13, 12, 13, 10, 13, 12, 6, 10, 9, 8, 12, 9, 10, 9, 5, 13, 10, 8, 10, 12, 6, 10, 8, 5, 10, 12, 10, 12, 13, 5, 5, 9, 6, 7, 10, 12, 8, 13, 13, 5, 7, 9, 9, 9, 7, 7, 10, 11, 4, 10, 8, 9, 10, 9, 11, 10, 5, 12, 7, 14, 10, 8, 6, 11, 5, 11, 14, 8, 7, 6, 10, 9, 5, 10, 11, 12, 7, 10, 10, 10, 8, 9, 10, 12, 5, 13, 9, 10, 8, 7, 9, 7, 3, 14, 8, 10, 8, 11, 9, 15, 9, 11, 9, 12, 7, 6, 11, 11, 12, 6, 9, 12, 9, 5, 10, 11, 8, 4, 9, 12, 8, 5, 8, 10, 8, 9, 4, 13, 10, 10, 13, 11, 8, 11, 8, 11, 12, 9, 5, 7, 10, 11, 12, 14, 9, 11, 8, 7, 10, 6, 7, 10, 12, 9, 9, 12, 9, 12, 10, 11, 9, 6, 6, 10, 8, 10, 6, 10, 11, 9, 9, 13, 10, 8, 11, 10, 6, 10, 7, 13, 12, 9, 8, 9, 13, 6, 3, 9, 4, 7, 13, 7, 5, 10, 8, 10, 13, 4, 6, 11, 6, 9, 10, 9, 15, 9, 9, 11, 10, 10, 9, 6, 9, 7, 13, 7, 7, 12, 10, 11, 8, 6, 9, 4, 13, 11, 6, 8, 8, 13, 12, 4, 9, 8, 14, 11, 12, 8, 13, 10, 14, 13, 8, 6, 8, 11, 8, 11, 10, 10, 10, 7, 10, 11, 6, 12, 11, 11, 14, 13, 9, 7, 4, 8, 12, 5, 5, 7, 9, 9, 11, 6, 13, 10, 6, 10, 8, 8, 10, 7, 9, 10, 2, 12, 11, 8, 7, 5, 11, 12, 4, 11, 10, 12, 11, 7, 10, 4, 9, 10, 7, 4, 13, 11, 12, 9, 4, 6, 8, 10, 8, 9, 8, 12, 10, 13, 7, 9, 9, 6, 9, 11, 5, 6, 9, 11, 9, 12, 12, 10, 10, 10, 10, 11, 10, 10, 8, 14, 11, 8, 11, 5, 9, 7, 10, 9, 7, 8, 14, 9, 7, 13, 7, 8, 11, 6, 11, 6, 6, 12, 9, 13, 10, 10, 12, 4, 11, 8, 11, 9, 10, 8, 11, 9, 7, 13, 7, 12, 11, 10, 9, 10, 11, 8, 8, 9, 12, 10, 12, 9, 10, 7, 9, 12, 9, 10, 8, 12, 5, 10, 11, 13, 8, 9, 7, 7, 3, 7, 12, 6, 10, 7, 8, 9, 9, 14, 5, 8, 15, 7, 5, 9, 11, 6, 8, 12, 9, 9, 9, 13, 8, 14, 11, 5, 7, 8, 12, 9, 10, 10, 13, 8, 11, 8, 15, 10, 4, 6, 10, 9, 9, 7, 13, 11, 8, 10, 12, 10, 7, 6, 6, 14, 11, 10, 7, 13, 12, 7, 10, 5, 9, 14, 5, 11, 7, 10, 10, 9, 8, 8, 10, 13, 7, 11, 8, 7, 8, 10, 9, 6, 11, 12, 8, 6, 11, 10, 9, 11, 12, 8, 10, 7, 10, 9, 8, 13, 7, 7, 13, 13, 12, 5, 11, 8, 10, 7, 9, 10, 9, 10, 8, 11, 12, 11, 5, 13, 12, 6, 11, 12, 12, 9, 13, 11, 9, 7, 12, 7, 11, 11, 7, 4, 8, 7, 7, 12, 12, 9, 12, 9, 5, 11, 9, 12, 6, 12, 7, 6, 8, 8, 10, 5, 7, 12, 10, 8, 8, 4, 6, 9, 11, 12, 8, 7, 9, 14, 12, 9, 7, 13, 9}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 9, 5, 7, 8, 6, 7, 6, 7, 7, 11, 10, 13, 9, 5, 10, 12, 8, 10, 11, 11, 9, 8, 10, 5, 11, 6, 5, 11, 9, 4, 7, 13, 9, 8, 7, 4, 11, 12, 2714575, 9, 10, 6, 9, 6, 10, 11, 12, 3, 8, 7, 8, 10, 12, 5, 8, 9, 7, 9, 9, 10, 7, 9, 10, 10, 11, 5, 6, 12, 8, 8, 9, 6, 9, 12, 7, 7, 11, 6, 6, 7, 12, 9, 8, 8, 9, 10, 6, 9, 9, 8, 9, 9, 6, 13, 11, 11, 9, 6, 12, 6, 8, 10, 10, 5, 4, 5, 10, 11, 6, 8, 6, 12, 7, 11, 6, 4, 10, 8, 9676, 9, 10, 9, 6, 8, 10, 7, 8, 10, 8, 4, 11, 6, 1468180, 12, 8, 10, 8, 5, 7, 10, 10, 7, 10, 10, 7, 5, 7, 9, 9, 7, 8, 11, 10, 9, 8, 10, 7, 5, 6, 9, 10, 14, 6, 6, 11, 6, 10, 7, 11, 11, 9, 8, 9, 11, 5, 7, 10, 5, 10, 9, 8, 6, 12, 7, 9, 9, 6, 5, 6, 9, 12, 11, 5, 14, 10, 7, 9, 11, 6, 8, 10, 7, 6, 8, 10, 5, 5, 6, 6, 8, 10, 9, 9, 10, 12, 29186362, 11, 8, 5, 6, 10, 7, 7, 10, 9, 9, 9, 14, 11, 45583023, 11, 9, 6, 10, 9, 5, 10, 6, 5, 8, 6, 10, 9, 10, 5, 8, 5, 5353, 10, 10, 6, 7, 7, 4, 5, 9, 11, 8, 5, 8, 15, 6, 10, 9, 10, 6494679, 7, 9, 8, 10, 5, 7, 7, 8, 10, 7, 10, 5, 10, 11, 10, 5, 9, 6, 9, 8, 6, 5, 9, 10, 10, 8, 14271325, 13, 11, 6, 9, 11, 9, 5, 8, 5, 9, 7, 8, 8, 9, 8, 80296, 11, 6, 7, 8, 14, 13, 7, 9, 6, 5, 7, 7, 8, 10, 6, 8, 10, 7, 6, 4, 1479, 16775347, 9, 10, 9, 8, 10, 6, 11, 6, 10, 7, 11, 7, 10, 9, 11, 6, 4, 10, 12, 7, 7, 8, 8, 8, 10, 6, 9, 9, 8, 10, 8, 9, 9, 13, 5, 12, 7, 6, 9, 9, 9, 6, 6, 10, 6, 10, 9, 11, 5, 8, 5, 9, 12, 8, 8, 7, 3, 6, 6, 8, 5, 8, 5, 9, 8, 11, 10, 5, 6, 7, 6, 6, 9, 9, 10, 6, 10, 8, 5, 7, 12, 4, 10, 8, 6, 8, 5, 11, 9, 11, 7, 11, 10, 11, 8, 10, 5, 9, 9, 10, 6, 11, 7, 9, 10, 8, 8, 13, 9, 7, 6, 10, 7, 11, 9, 8, 10, 9, 8, 9, 7, 8, 9, 9, 8, 7, 9, 7, 7, 12, 5, 7, 11, 4, 8, 8, 15, 11, 11, 8, 5, 7, 11, 9, 5, 8, 8, 12, 9, 9, 7, 9, 6, 12, 10, 9, 8, 5, 9, 6, 216300003, 6, 10, 6, 4, 6, 9, 5, 5, 11, 11, 11, 7, 9, 8, 13, 11, 8, 7, 5, 10, 8, 8, 10, 9, 6, 8, 7, 7, 11, 9, 8, 5, 9, 12, 9, 7, 10, 10, 8, 11, 11, 11, 5, 6, 5, 6, 7, 6, 11, 10, 8, 6, 5, 11, 6, 9, 11, 12, 8, 6, 12, 9, 2619, 7, 8, 8, 13, 8, 6, 9, 6, 8, 237954, 12, 9, 12, 6, 7, 9, 6, 12, 5, 9, 8, 9, 8, 10, 6, 11, 11, 6, 11, 11, 13, 5, 8, 10, 5, 10, 9, 7, 7, 7, 11, 4, 12, 8, 11, 6, 12, 9, 6, 8, 8, 11, 8, 12, 10, 6, 11, 12, 9, 11, 9, 9, 5, 9, 9, 8, 5, 5, 47501, 7, 12, 5, 10, 7, 12, 10, 8, 15, 8, 10, 7, 13, 10, 10, 10, 13, 9, 12, 10, 6, 10, 7, 7, 6, 7, 13, 11, 9, 7, 7, 12, 7, 12, 7, 4, 5, 11, 2248, 11, 8, 7, 9, 10, 8, 11, 9, 8, 9, 9, 9, 7, 10, 11, 6, 9, 6, 11, 6, 2047, 8, 10, 9, 10, 10, 6, 8, 6, 8, 9, 7, 7, 11, 10, 11, 12, 10, 7, 9, 12, 11, 6, 7, 6, 7, 10, 8, 6, 460908, 11, 7, 8, 8, 9, 8, 7, 12, 5, 10, 6, 11, 12, 6, 7, 6, 11, 8, 4, 7, 12, 9, 10, 6, 13, 5, 11, 4, 6, 8, 8, 9, 6, 7, 11, 8, 9, 6, 8, 11, 7, 9, 10, 9, 7, 10, 7, 9, 9, 11, 7, 9, 8, 11, 8, 9, 6, 11, 12, 9, 9, 10, 9, 9, 8, 8, 5, 10, 7, 8, 7, 9, 8, 8, 8, 9, 8, 9, 6, 10, 7, 7, 8, 6, 7, 6, 7, 4, 8, 7, 13, 5, 25241917, 11, 10, 5, 10, 9, 9, 5, 10, 8, 6, 2, 6, 7, 101152483, 6, 11, 7, 11, 11, 10, 5, 8, 9, 7, 9, 7, 10, 8, 59192, 10, 7, 7, 9, 8, 5, 9, 9, 9, 7, 6, 7, 7, 12, 9, 8, 7, 12, 8, 10, 8, 9, 12, 11, 8, 11, 4, 6, 5, 7, 2160591, 8, 10, 12, 11, 9, 1049, 8, 7, 10, 5, 9, 6, 11, 10, 9, 5, 5, 12, 12, 7, 10, 7, 11, 6, 10, 7, 8, 10, 9, 10, 7, 7, 7, 10, 6, 8, 8, 9, 11, 5, 6, 5, 8, 9, 13, 11, 7, 13, 8, 5, 10, 7, 11, 5, 11, 12, 7, 11, 9, 10, 4, 9, 14, 11, 10, 11, 9, 12, 11, 10, 7, 10, 9, 7, 9, 10, 6, 10, 8, 8, 8, 6, 8, 13, 6, 8, 6, 6, 9, 10, 7, 48404722, 10, 7, 9, 9, 11, 10, 8, 11, 10, 8, 725476, 8, 9, 7, 10, 12, 9, 7, 8, 8, 6, 6, 10, 7, 5, 11, 11, 13, 7, 10, 11, 6, 4, 10, 5, 5, 5, 9, 9, 64499869}

Returns: {2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2 }
{12, 6, 9, 11, 6, 7, 9, 7, 9, 12, 12, 12, 11, 6, 10, 17, 10, 8, 10, 7, 8, 11, 9, 11, 9, 10, 8, 11, 15, 16, 12, 12, 9, 11, 15, 10, 12, 12, 13, 6, 9, 10, 11, 11, 9, 207824, 13, 11, 12, 9, 12, 8, 14, 11, 13, 9, 10, 15, 12, 8, 10, 5, 12, 13, 5, 10, 11, 13, 11, 13, 10, 11, 8, 9, 12, 14, 8, 10, 5, 7, 11, 13, 10, 14, 8, 9, 6, 9, 12, 11, 6, 14, 9, 14, 14, 13, 8, 10, 14, 12, 10, 10, 6, 12, 11, 12, 12, 12, 12, 11, 15, 10, 13, 2971701, 10, 12, 12, 5, 3, 10, 9, 9, 13, 11, 12, 12, 7, 12, 10, 8, 9, 12, 11, 10, 7, 8, 8, 12, 11, 7, 5, 10, 7, 7, 12, 12, 8, 8, 10, 7, 12, 12, 10, 3, 11, 7, 8, 12, 12, 14, 7, 15, 14, 9, 10, 9, 10, 9, 9, 7, 11, 9, 13, 11, 9, 10, 12, 11, 8, 11, 7, 11, 11, 5, 14, 10, 14, 10, 14, 13, 3, 13, 9, 10, 13, 12, 11, 6, 13, 8, 9, 13, 11, 13, 10, 16, 13, 8, 13, 15, 11, 14, 10, 11, 13, 5, 11, 2, 9, 10, 12, 16, 10, 12, 9, 17, 9, 10, 11, 12, 14, 9, 8, 8, 15, 10, 12, 10, 6, 9, 6, 358796, 12, 14, 12, 13, 12, 6, 10, 9, 16, 13, 11, 9, 13, 5, 12, 10, 7, 5, 9, 14, 10, 8, 30588, 7, 6, 15, 7, 6, 14, 11, 13, 11, 9, 12, 13, 12, 10, 14, 9, 10, 10, 6, 9, 14, 8, 10, 10, 8, 12, 5, 14, 13, 12, 7, 13, 12, 11, 14, 9, 12, 14, 13, 11, 7, 12, 7, 12, 10, 11, 9, 8, 77009, 9, 9, 8, 11, 9, 13, 13, 7, 7, 14, 11, 11, 9, 8, 7, 12, 10, 6, 15, 7, 10, 7, 8, 10, 9, 7, 5, 54453, 6, 9, 13, 4, 8, 8, 11, 9, 6, 9, 12, 12, 13, 9, 9, 14, 13, 10, 11, 9, 13, 13, 6, 13, 9, 12, 7, 9, 11, 10, 12, 10, 9, 14, 9, 13, 10, 10, 6, 8, 10, 12, 8, 12, 9, 14, 10, 16, 8, 10, 12, 12, 10, 11, 9, 11, 6, 5, 4, 11, 5, 8, 12, 9, 8, 9, 5, 6, 12, 12, 6, 11, 15, 12, 7, 11, 13, 11, 8, 12, 11, 6, 8, 10, 9, 6, 3, 12, 15, 8, 7, 13, 7, 8, 11, 11, 11, 8, 14, 13, 12, 11, 10, 9, 8, 11, 126560444, 9, 10, 11, 13, 12, 8, 12, 11, 11, 10, 13, 6, 10, 14, 6, 9, 8, 4, 6, 7, 9, 14, 12, 11, 12, 9, 14, 6, 8, 15, 12, 7, 9, 12, 7, 16, 13, 12, 10, 12, 12, 10, 7, 1301, 7, 2, 10, 11, 11, 11, 7, 8, 10, 7, 9, 10, 10, 11, 13, 9, 8, 12, 143122, 9, 8, 10, 12, 10, 7, 11, 12, 14, 8, 9, 6, 10, 8, 6, 8, 14, 11, 10, 9, 10, 8, 16, 9, 9, 12, 13, 12, 9, 7, 11, 9, 10, 11, 9, 11, 12, 14, 7, 13, 11, 12, 17, 12, 13, 9, 9, 10, 9, 13, 12, 12, 10, 9, 11, 14, 10, 8, 10, 13, 10, 9, 8, 266765469, 12, 14, 4, 7, 12, 17, 12, 8, 9, 11, 12, 96424, 12, 11, 5, 12, 12, 9, 8, 12, 11, 8, 6, 16, 3, 17, 6, 560462, 11, 9, 12, 11, 13, 5, 12, 12, 11, 7, 10, 8, 11, 11, 8, 9, 11, 11, 8, 12, 12, 10, 8, 15, 6, 10, 8, 15, 6, 10, 9, 8, 11, 8, 10, 8, 11, 11, 10, 8, 13, 9, 16, 11, 11, 12, 10, 13, 8, 6, 14, 11, 8, 8, 12, 10, 11, 6, 11, 10, 9, 9, 9, 6, 10, 10, 9, 12, 7, 14, 12, 7, 12, 6, 10, 13, 11, 12, 15, 6, 14, 8, 8, 9, 10, 3, 11, 10, 14, 10, 13, 9, 6, 10, 12, 10, 7, 10, 6, 9, 12, 6, 8, 13, 6, 9, 15, 14, 14, 8, 13, 7, 10, 4, 9, 10, 9, 14, 9, 11, 7, 11, 9, 13, 12, 12, 11, 6, 13, 8, 12, 10, 7, 9, 14, 10, 11, 9, 13, 9, 11, 10, 13, 11, 12, 6, 9, 6, 13, 12, 14, 13, 8, 10, 7, 8, 8, 9, 13, 8, 8, 13, 8, 15, 11, 14, 10, 14, 7, 11, 9, 14, 11, 8, 13, 3, 13, 7, 14, 13, 13, 13, 10, 8, 8, 9, 13984357, 13, 12, 10, 10, 9, 6, 13, 2, 9, 6, 8, 8, 9, 10, 9, 12, 12, 8, 9, 9, 6, 11, 4, 9, 14, 12, 6, 11, 16, 12, 10, 11, 12, 9, 2, 13, 13, 10, 11, 12, 13, 9, 8, 9, 11, 13, 6, 14, 10, 7, 12, 8, 10, 10, 12, 8, 7, 11, 8, 5, 12, 7, 10, 9, 9, 9, 8, 12, 9, 12, 11, 14, 7, 13, 17, 9, 11, 15, 16, 9, 8, 5, 8, 12, 7, 10, 15, 10, 6, 11, 6, 11, 7, 7, 15, 9, 4, 10, 8, 8, 9, 13, 12, 1300, 14, 7, 10, 11, 9, 16, 7, 10, 12, 12, 9, 8, 8, 7, 14, 9, 10, 16, 13, 38012391, 13, 13, 9, 6, 9, 12, 11, 5, 10, 9, 7, 11, 7, 9, 9, 8, 14, 12, 8, 12, 12, 11, 13, 10, 10, 11, 10, 15, 13, 11, 366863, 12, 8, 7, 11, 9, 7, 14, 10, 8, 9, 6, 9, 8, 6, 10, 14, 14, 10, 15, 13, 10}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 9, 7, 7, 7, 6, 8, 7, 8, 11, 6, 6, 4, 8, 7, 10, 5, 12, 10, 11, 5, 8, 8, 9, 11, 8, 9, 6, 8, 10, 8, 10, 14, 7, 8, 9, 9, 9, 3, 6, 7, 9, 10, 10, 8, 5, 8, 7, 9, 33549339, 5, 6, 9, 10, 7, 6, 8, 7, 9, 10, 7, 9, 11, 8, 9, 7, 10, 10, 7, 7, 7, 5, 7, 6, 7, 9, 5, 12, 5, 6, 7, 9, 10, 11, 7, 8, 7, 11, 7, 8, 8, 5, 12, 8, 8, 6, 6, 8, 8, 10, 9, 11, 12, 7, 7, 8, 6, 8, 8, 8, 8, 9, 9, 7, 7, 12, 7, 9, 8, 8, 7, 11, 6, 8, 10, 7, 8, 10, 7, 9, 8, 11, 14, 7, 12, 9, 8, 7, 9, 11, 9, 6, 11, 10, 9, 9, 9, 8, 6, 7, 7, 6, 9, 16, 8, 8, 9, 5732541, 8, 7, 11, 13, 7, 7, 10, 13, 4, 10, 7, 7, 10, 7, 7, 7, 8, 13, 10, 11, 7, 10, 7, 9, 9, 9, 10, 7, 9, 6, 5, 8, 8, 8, 7, 6, 7, 7, 9, 12, 6, 11, 8, 7, 11, 12, 8, 8, 24125040, 11, 8, 8, 11, 9, 9, 7, 9, 10, 9, 7, 6, 4, 14, 6, 7, 9, 4171208, 9, 11, 9, 11, 10, 8, 11, 9, 7, 7, 7, 10, 7, 12, 9, 9, 9, 8, 8, 7, 8, 9, 8, 13, 13, 8, 7, 10, 8, 8, 5, 9, 5, 8, 316378309, 6, 7, 9, 7, 7, 8, 8, 6, 10, 7, 12, 9, 7, 13, 8, 9, 8, 7, 6, 13, 7, 4, 9, 8, 9, 8, 9, 6, 11, 7, 9, 6, 6, 9, 7, 8, 3, 8, 7, 11, 9, 7, 9, 7, 8, 7, 10, 9, 8, 13, 9, 11, 7, 11, 8, 7, 8, 7, 7, 11, 8, 9, 9, 9, 8, 7, 9, 10, 6, 3, 7, 11, 14, 13, 8, 12, 10, 6, 10, 9, 8, 9, 10, 8, 9, 11, 4, 9, 7, 10, 11, 7, 11, 5, 8, 10, 8, 8, 9, 8, 8, 5, 10, 10, 14, 10, 9, 6, 5, 14, 10, 8, 12, 10, 10, 8, 7, 8, 11, 6, 7, 11, 8, 10, 8, 4, 6, 6, 9, 6, 10, 11, 8, 8, 13, 9, 10, 3, 10, 10, 8, 14, 8, 12, 6, 8, 6, 7, 5, 9, 10, 8, 5, 11, 15, 10, 8, 10, 10, 10, 9, 9, 6, 9, 7, 6, 8, 10, 11, 9, 5, 8, 10, 12, 8, 9, 7, 5, 10, 16, 9, 10, 8, 9, 12, 7, 5, 11, 5, 8, 8, 8, 5, 6, 8, 5, 12, 8, 9, 6, 10, 5, 8, 8, 9, 7, 10, 9, 8, 8, 11, 5, 6, 13, 12, 9, 7, 10, 8, 7, 11, 9, 9, 10, 8, 6, 12, 7, 9, 8, 7, 6, 9, 9, 9, 6, 6, 9, 6, 7, 8, 8, 12, 9, 7, 6, 8, 9, 6, 7, 10, 9, 11, 9, 11, 5, 10, 12, 11, 8, 7, 6, 9, 8, 9, 11, 7, 9, 7, 6, 4, 7, 7, 11, 11, 10, 10, 8, 8, 8, 7, 4, 4, 7, 6, 9, 8, 10, 6, 14, 7, 9, 7, 9, 7, 6, 12, 6, 9, 6, 7, 9, 9, 6, 6, 8, 8, 13, 9, 6, 5, 5, 7, 10, 8, 11, 8, 10, 8, 11, 9, 11, 9, 6, 6, 6, 11, 9, 5, 7662, 6, 4, 9, 9, 10, 8, 11, 9, 11, 9, 9, 9, 5, 6, 8, 10, 10, 10, 9, 11, 8, 10, 11, 6, 7, 11, 8, 10, 10, 8, 10, 8, 7, 8, 10, 7, 23853046, 11, 11, 8, 12, 7, 8, 8, 11, 13, 12, 7, 10, 6, 6, 11, 11, 9, 14, 7, 4, 7, 6, 4, 9, 10, 8, 11, 9, 9, 2, 8, 6, 7, 6, 11, 6, 9, 7, 8, 8, 9, 10, 10, 10, 7, 9, 8, 6, 9, 8, 7, 8, 10, 12, 8, 8, 5, 8, 6, 9, 11, 2915, 10, 11, 7, 9, 11, 8, 8, 10, 10, 9, 6, 9, 7, 8, 6, 6, 12, 8, 13, 8, 11, 8, 5, 7, 7, 8, 7, 15, 8, 11, 8, 6, 7, 11, 9, 8, 11, 8, 9, 9, 5, 9, 12, 11, 7, 9, 6, 10, 11, 8, 8, 7, 5, 8, 7, 4, 8, 7, 13, 8, 3, 6, 7, 9, 9, 5, 9, 7, 11, 9, 5, 9, 10, 9, 11, 8, 5, 6, 8, 10, 9, 5, 8, 9, 9, 7, 7, 11, 7, 6, 9, 10, 9, 11, 6, 10, 7, 7, 8, 10, 8, 5, 6, 5, 9, 6, 9, 14, 7, 6, 6, 10, 5, 10, 7, 8, 6, 10, 10, 7, 8, 6, 5, 8, 8, 6, 9, 8, 5, 7, 7, 8, 7, 9, 11, 5, 6, 9, 6, 9, 8, 9, 9, 9, 6, 10, 9, 8, 10, 11, 6, 9, 9, 7, 7, 8, 9, 6, 10, 5, 8, 11, 6, 14, 9, 8, 8, 8, 10, 11, 9, 5, 8, 6, 11, 6, 12, 7, 10, 6559, 12, 8, 10, 8, 7, 5, 9, 12, 11, 6, 11, 8, 7, 9, 7, 6, 8, 9, 5, 5, 8, 6, 8, 10, 9, 11, 6, 9, 10, 9, 9, 10, 14, 4, 9, 6, 7, 3, 9, 6, 13, 10, 8, 10, 10, 9, 7, 7, 4, 8, 6, 5, 9, 11, 8, 8, 10, 8, 10, 5, 8, 11, 9, 7, 9, 9, 12, 11, 14, 11, 5, 7, 6, 10, 7, 7, 8, 6, 11, 9, 9, 10, 8, 9, 9, 9, 14, 5, 7, 7, 8, 6, 8, 7, 9, 8, 8, 9, 10, 5, 5, 9, 12, 7, 11, 16, 6, 10, 8, 10, 8, 8, 9, 12, 7}

Returns: {-1 }
{10, 7, 11, 6, 9, 12, 9, 8, 11, 9, 10, 9, 8, 11, 12, 7, 10, 7, 7, 6, 9, 10, 10, 10, 14, 10, 8, 9, 8, 6, 8, 10, 5, 10, 9, 10, 10, 5, 6, 10, 13, 9, 9, 8, 6, 10, 11, 6, 15, 9, 9, 10, 10, 8, 12, 6, 11, 6, 10, 9, 8, 12, 8, 5, 8, 10, 12, 7, 8, 6, 5, 6, 10, 8, 6, 10, 8, 8, 11, 9, 5, 4, 7, 6, 9, 10, 6, 5, 12, 10, 9, 9, 7, 12, 10, 8, 7, 8, 10, 10, 13, 12, 6, 8, 7, 9, 12, 9, 12, 5, 12, 6, 8, 11, 5, 6, 10, 12, 9, 9, 10, 12, 8, 13, 8, 11, 14, 6, 7, 10, 11, 7, 7, 6, 7, 11, 12, 10, 9, 11, 11, 11, 10, 10, 7, 7, 15, 8, 5, 8, 7, 8, 8, 9, 7, 6, 12, 10, 9, 15, 9, 13, 6, 9, 4, 11, 7, 6, 5, 8, 8, 9, 9, 11, 8, 7, 9, 7, 6, 7, 7, 12, 8, 11, 12, 11, 6, 11, 9, 5, 6, 11, 7, 7, 9, 4, 10, 7, 10, 7, 7, 7, 13, 12, 6, 12, 3, 10, 6, 10, 10, 6609091, 14, 4, 9, 12, 10, 4, 12, 7, 8, 10, 6, 12, 10, 7, 5, 5, 6, 6, 8, 13, 16, 12, 12, 8, 10, 10, 8, 7, 8, 13, 15, 10, 5, 10, 7, 7, 7, 9, 6, 9, 8, 15, 13, 13, 1762407, 9, 4, 12, 5, 9, 5, 83250, 11, 11, 13, 9, 7, 23273187, 11, 65758969, 6, 12, 9, 6, 11, 7, 7, 8, 9, 13, 11, 8, 7, 14, 15, 10, 7, 8, 9, 14, 8, 9, 4, 11, 9, 8, 11, 7, 7, 9, 13, 6, 12, 9, 13, 13, 11, 12, 10, 8, 12, 9, 9, 14, 7, 7, 12, 4, 5, 5, 10, 14, 437456, 6, 6, 11, 10, 10, 8, 7, 10, 15, 6, 9, 6, 4, 12, 522811721, 10, 11, 10, 11, 10, 8, 9, 7, 10, 5, 7, 8, 14, 9, 9, 5, 11, 8, 5, 7, 11, 10, 9, 8, 9, 6, 8, 14, 8, 10, 13, 7, 7, 8, 7, 11, 7, 9, 5, 10, 7, 9, 3, 10, 7, 9, 10, 10, 9, 12, 10, 7, 7, 12, 9, 5, 7, 8, 9, 10, 9, 15, 8, 12, 7, 9, 8, 4, 7, 6, 15, 8, 9, 10, 11, 7, 8, 14, 12, 6, 9, 15, 7, 10, 6, 11, 8, 11, 14, 14, 7, 3, 5, 7, 7, 10, 13, 8, 12, 10, 9, 5, 7, 9, 9, 10, 7, 4, 12, 13, 8, 14, 10, 7, 8, 9, 5, 11, 9, 6, 10, 8, 11, 9, 12, 5, 6, 9, 9, 9, 10, 12, 5, 9, 11, 7, 7, 9, 7, 8, 10, 9, 5, 4, 5, 9, 15, 13, 7, 4, 7, 10, 14, 8, 9, 6, 14, 9, 6, 12, 11, 12, 6, 9, 12, 7, 6, 14, 9, 2, 9, 16, 11, 4, 15, 5, 7, 9, 10, 7, 10, 6, 10, 10, 11, 6, 7, 8, 9, 10, 7, 10, 10, 7, 9, 9, 8, 10, 8, 8, 7, 9, 5, 7, 12, 6, 8, 6, 7, 12, 10, 4, 5, 10, 13, 10, 8, 9, 10, 7, 11, 11, 10, 6, 6, 8, 10, 11, 10, 14, 110844857, 8, 6, 9, 6, 11, 9, 10, 7, 5, 4, 10, 7, 14, 14, 13, 5, 12, 11, 9, 8, 10, 9, 10, 8, 8, 12, 14, 9, 7, 10, 5, 11, 7, 6, 9, 7, 6, 10, 4, 7, 6, 8, 5, 6, 9, 12, 10, 9, 12, 7, 8, 8, 7, 5, 13, 10, 11, 9, 4, 14, 12, 14, 10, 9, 9, 6, 5, 9, 4, 9, 9, 9, 9, 11, 10, 9, 10, 7, 8, 5, 8, 7, 7, 7, 11, 7, 14, 13, 7, 7, 7, 10, 8, 11, 10, 5, 12, 8, 11, 11, 12, 10, 6, 14, 11, 11, 6, 9, 9, 11, 12, 10, 13, 6, 6, 11, 10, 9, 7, 9, 10, 10, 11, 11, 8, 10, 6, 9, 10, 11, 10, 14, 10, 10, 10, 6, 6, 9, 8, 13, 7, 9, 11, 5, 11, 6, 6, 4, 9, 10, 8, 10, 13, 10, 11, 6, 15, 8, 9, 7, 12, 8, 8, 9, 7, 8, 5, 9, 8, 12, 9, 4, 4, 12, 6, 5, 6, 7, 10, 9, 8, 11, 7, 8, 11, 4, 6, 5, 26228, 7, 6, 7, 6, 14, 7, 4, 11, 10, 13, 10, 11, 8, 6, 6, 12, 8, 9, 9, 7, 9, 11, 12, 11, 4, 11, 8, 6, 15, 11, 11, 11, 9, 9, 9, 8, 10, 10, 9, 9, 7, 7, 14, 8, 11, 11, 9, 8, 11, 7, 13, 7, 13, 133590896, 10, 7, 12, 14, 13, 8, 8, 9, 10, 10, 11, 5, 7, 8, 7, 14, 8, 11, 8, 7, 11, 7, 9, 14, 10, 10, 11, 10, 11, 10, 6, 10, 6, 9, 12, 9, 10, 9, 12, 5, 10, 11, 10, 8, 8, 13, 11, 4, 12, 11, 5, 9, 9, 6, 10, 8, 7, 10, 6, 10, 10, 8, 6, 8, 6, 9, 5, 9, 24699791, 7, 10, 10, 9, 10, 8, 14, 10, 16, 12, 10, 5, 7, 4, 7, 10, 10, 10, 13, 9, 7, 8, 11, 9, 9, 10, 8, 8, 12, 7, 7, 5, 12, 11, 11, 9, 7, 7, 11, 6, 11, 8, 10, 7, 8, 6, 10, 6, 8, 6, 9, 10, 11, 8, 12, 9, 10, 7, 10, 9, 8, 9, 10, 14, 8, 14, 10, 12, 8, 8, 6, 10, 8, 8, 9, 12, 14, 9, 8, 10, 6, 9, 10, 6, 10, 8, 11, 11, 11, 10, 11, 12, 9, 5, 11, 7, 7, 8, 11, 11, 12, 7, 10, 10, 9, 6, 4, 6, 7, 13, 6}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2 }
{6, 9, 10, 12, 9, 9, 6, 10, 7, 10, 10, 14, 5, 10, 7, 11, 8, 9, 10, 6, 12, 13, 5, 11, 8, 11, 13, 8, 10, 15, 12, 11, 10, 8, 11, 6, 8, 8, 7, 8, 8, 6, 8, 8, 13, 14, 16, 9, 7, 7, 6, 15, 11, 13, 4, 10, 8, 14, 13, 7, 16, 7, 5, 13, 12, 10, 8, 11, 2, 8, 8, 15, 14, 11, 8, 8, 8, 13, 14, 12, 14, 9, 8, 11, 8, 7, 7, 10, 8, 14, 11, 9, 12, 7, 13, 8, 8, 13, 12, 8, 11, 9, 7, 8, 8, 2, 10, 9, 12, 11, 12, 10, 15, 12, 8, 11, 7, 4, 5, 7, 15, 12, 8, 11, 12, 12, 10, 11, 3, 65124, 12, 10, 14, 9, 10, 12, 9, 14, 14, 8, 14, 14, 11, 9, 12, 9, 9, 10, 12, 14, 8, 14, 12, 11, 9, 14, 12, 13, 7, 10, 9, 11, 5, 15, 15, 5, 11, 16, 12, 9, 10, 8, 11, 7, 11, 16, 3, 86495458, 10, 10, 9, 15, 12, 7, 9, 12, 12, 6, 8, 12, 8, 11, 10, 9, 9, 11, 9, 8, 8, 10, 10, 8, 6, 3, 8, 9, 11, 7, 10, 15, 3, 9, 8, 17, 8, 9, 10, 14, 12, 3, 10, 5, 8, 12, 11, 16, 8, 8, 10, 15, 6, 7, 11, 11, 8, 13, 11, 10, 9, 7, 8, 11, 9, 8, 14, 10, 16, 13, 14, 8, 11, 7, 8, 12, 8, 8, 6, 11, 26885, 12, 8, 9, 12, 8, 11, 10, 9, 9, 13, 10, 9, 7, 12, 15, 12, 10, 8, 9, 4, 10, 8, 10, 8, 7, 12, 9, 10, 6, 11, 9, 9, 10, 9, 436573, 9, 12, 10, 11, 11, 10, 14, 9, 10, 6, 12, 11, 10, 9, 9, 14, 6, 9, 14, 16, 13, 14, 11, 10, 8, 9, 8, 9, 6, 9, 12, 11, 9, 8, 6, 7, 7, 13, 14, 11, 15, 12, 13, 10, 9, 9, 9, 8, 9, 12, 11, 9, 8, 7, 11, 9, 15, 6, 8, 8, 15, 9, 15, 8, 11, 11, 11, 14, 11, 11, 5, 9, 5, 10, 10, 11, 6, 9, 15, 9, 15, 12, 11, 11, 8, 9, 9, 10, 11, 8, 8, 6, 9, 6, 10, 10, 14, 15, 9, 7, 11, 11, 6, 14, 11, 7, 15, 8, 12, 11, 14, 7, 11, 11, 8, 12, 11, 7, 7857, 3, 8, 10, 15, 6, 10, 9, 9, 7, 9, 11, 10, 13, 11, 9, 9, 10, 9, 14, 5, 14, 10, 12, 10, 7, 8, 9, 11, 12, 9, 7, 14, 11, 6, 15, 9, 8, 9, 6, 11, 11, 10, 11, 12, 8, 2320329, 8, 8, 6, 14, 12, 8, 9, 9, 12, 11, 13, 11, 7, 10, 14, 57091378, 5, 8, 9, 8, 11, 7, 4, 10, 12, 7, 12, 15, 11, 9, 10, 7, 12, 15, 17, 15, 13, 9, 6, 11, 8, 11, 15, 11, 15, 6, 11, 5, 11, 9, 11, 11, 12, 14, 12, 15, 11, 15, 9, 11, 8, 9, 16, 7, 9, 14, 11, 12, 10, 13, 10, 9, 7, 11, 8, 11, 11, 8, 14, 7, 8, 15, 12, 6, 6, 10, 9, 11, 9, 7, 11, 10, 9, 9, 7, 10, 11, 15, 8, 9, 10, 11, 8, 15, 6, 10, 15, 9, 9, 12, 8, 9, 11, 11, 10, 8, 13, 10, 7, 9, 9, 10, 9, 8, 6, 11, 9, 11, 11, 8, 8, 11, 13, 8, 7, 10, 9, 11, 3, 7, 8, 7, 10, 13, 5, 5, 6, 6, 10, 5, 10, 11, 9, 15, 9, 7, 13, 12, 12, 8, 12, 12, 10, 8, 7, 7, 11, 8, 9, 7, 7, 6, 7, 11, 10, 12, 12, 14, 10, 11, 8, 8, 8, 8, 8, 13, 7, 14, 11, 10, 11, 10, 11, 8, 4, 9, 9, 16, 12, 8, 12, 12, 9, 8, 10, 12, 6, 12, 8, 11, 9, 15, 8, 10, 9, 5, 15, 8, 9, 11, 15, 10, 13, 11, 14, 8, 11, 8, 14, 6, 13, 7, 8, 11, 12, 8, 8, 11, 6, 9, 4, 11, 11, 7, 10, 13, 2, 8, 9, 10, 10, 10, 10, 13, 7, 12, 10, 12, 10, 8, 9, 13, 14, 11, 13, 11, 12, 12, 8, 11, 8, 10, 11, 12, 13, 6, 11, 8, 7, 11, 9, 12, 14, 15, 7, 10, 11, 12, 7, 12, 15, 11, 15, 11, 11, 11, 16, 5, 8, 11, 7, 6, 14, 12, 9, 9, 10, 5, 8, 7, 9, 9, 11, 11, 8, 11, 10, 11, 7, 13, 11, 11, 12, 11, 7, 9, 8, 17, 11, 8, 8, 6, 12, 11, 13, 14, 7, 11, 11, 16, 10617508, 11, 11, 6, 12, 8, 12, 9, 9, 10, 8, 9, 8, 9, 7, 7, 8, 15, 10, 11, 11, 12, 10, 14, 9, 10, 10, 10, 12, 11, 8, 6, 9, 10, 255298827, 9, 10, 11, 6, 7, 13, 15, 7, 12, 5, 12, 9, 5, 8, 10, 11, 7, 12, 8, 7, 10, 7, 7, 10, 8, 9, 9, 10, 11, 9, 8, 7, 13, 13, 6, 6, 11, 8, 9, 9, 14, 12, 12, 16368446, 11, 12, 6, 912413, 6, 6225216, 12, 6, 12, 10, 10, 11, 9, 2, 8, 9, 15, 7, 13, 12, 8, 13, 7, 12, 9, 11, 11, 9, 6, 9, 12, 11, 12, 9, 10, 9, 10, 11, 8, 9, 9, 10, 10, 7, 12, 12, 10, 13, 5, 8, 13, 10, 12, 11, 9, 12, 12, 14, 11, 9, 12, 7, 9, 13, 15, 9, 9, 10, 7, 9, 11, 11, 11, 10, 24043, 10, 12, 8, 6, 11, 11, 12, 12, 6, 9, 6, 11, 12, 11, 9, 15, 10, 9, 14}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{7, 12, 6, 11, 11, 12, 12, 9, 243040444, 9, 9, 10, 10, 8, 11, 10, 6, 7, 12, 9, 5, 9, 4, 13, 12, 9, 6, 12, 9, 7, 9, 8, 6, 11, 9, 4, 13, 13, 8, 14, 8, 11, 10, 10, 12, 9, 16, 21079, 12, 11, 9, 14, 5, 10, 6, 12, 10, 11, 8, 7, 10, 12, 8, 6, 8, 7, 5, 10, 10, 8, 8, 503397, 11, 11, 7, 8, 10, 5, 10, 11, 11, 6, 11, 6, 10, 9, 9, 14, 6, 9, 6, 7, 9, 7, 12, 13, 14, 8, 11, 12, 13, 9, 12, 13, 12, 9, 11, 8, 12, 9, 7, 5, 8415172, 7, 8, 5, 9, 8, 10, 8, 9, 9, 11, 8, 10, 12, 8, 3, 9, 1762, 11, 11, 10, 10, 11, 10, 11, 11, 8, 8, 14, 11, 11, 10, 9, 12, 12, 7, 10, 10, 11, 11, 9, 9, 10, 9, 9, 8, 9, 13, 14, 9, 11, 10, 12, 10, 8, 9, 7, 9, 7, 7, 11, 6, 10, 10, 7, 12, 9, 11, 9, 16, 14, 10, 14, 12, 48245, 12, 11, 12, 14, 5766, 12, 6, 10, 12, 8, 7, 14, 15, 12, 9, 8, 11, 15, 10, 5, 11, 11, 8, 10, 10, 10, 9, 11, 7, 12, 7, 10, 10, 9, 13, 15, 10, 7, 9, 8, 8, 9, 10, 8, 9, 8, 10, 12, 13, 12, 12, 8, 12, 11, 9, 12, 14, 12, 3, 9, 11, 11, 7, 9, 8, 12, 7, 8, 14, 10, 9, 9, 491862, 9, 6, 5570719, 8, 8, 11, 5, 15, 7, 11, 9, 11, 11, 12, 9, 6, 8, 14, 10, 9, 5, 12, 12, 9, 7, 9, 10, 10, 8, 8, 13, 10, 59483923, 5, 6, 9, 13, 12, 10, 9, 13, 14, 9, 6, 7, 13, 4, 9, 12, 8, 10, 9, 7, 13, 10, 7, 8, 13, 8, 7, 10, 10, 8, 14, 11, 5, 9, 12, 13, 11, 8, 12, 13, 11, 12, 13, 11, 7, 12, 8, 9, 12, 11, 7, 9, 11, 12, 10, 15, 6, 15, 8, 12, 12, 12, 6, 5, 4, 9, 9, 7, 10, 11, 8, 10, 12, 332479, 10, 9, 5, 14, 2, 9, 14, 8, 8, 8, 7, 13, 10, 8, 8, 6, 11, 11, 15, 9, 9, 14, 13, 11, 13, 9, 12, 8, 8, 459212662, 7, 9, 12, 14, 12, 9, 10, 9, 11, 9, 12, 9, 9, 7, 15, 14, 8, 11, 10, 7, 9, 10, 7, 7, 12, 8, 11, 9, 7, 12, 9, 4, 12, 10, 10, 14, 9, 12, 12, 12, 9, 12, 9, 6, 10, 12, 7, 13, 13, 15, 8, 9, 5, 11, 11, 15, 8, 10, 13, 7, 13, 12, 9, 10, 11, 8, 7, 9, 13, 102804908, 12, 9, 10, 11, 8, 7, 11, 12, 11, 8, 7, 10498, 13, 14, 4, 11, 11, 8, 11, 10, 7, 13, 14, 12, 7, 9, 12, 8, 8, 12, 14, 9, 8, 4, 4, 14, 7, 8, 8, 6, 13, 13, 9, 13, 10, 13, 6, 9, 8, 9, 8, 9, 10, 9, 9, 8, 8, 4, 62003, 6, 8, 6, 7, 3282443, 11, 10, 6, 8, 11, 12, 8, 7, 7, 9, 11, 11, 10, 6, 10, 9, 7, 11, 11, 8, 9, 7, 9, 9, 8, 9, 16, 10, 8, 13, 11, 10, 12, 12, 10, 8, 9, 14, 9, 8, 10, 7, 8, 9, 7, 10, 8, 6, 8, 10, 11, 10219325, 10, 6, 6, 11, 12, 11, 8, 8, 14, 6, 8, 10, 14, 7, 7, 9, 12, 8, 14, 8, 12, 7, 5, 12, 9, 10, 7, 6, 16, 12, 9, 11, 7, 7, 11, 14, 12, 7, 9, 2, 11, 11, 9, 13, 7, 8, 9, 9, 7, 9, 9, 11, 8, 8, 9, 10, 9, 13, 8, 9, 11, 12, 7, 8, 6, 14, 11, 8, 7, 10, 7, 12, 13, 7, 8, 10, 11, 10, 12, 9, 5081, 12, 11, 9, 10, 9, 8, 9, 14, 8, 10, 9, 12, 11, 10, 6, 10, 13, 10, 2749428, 10, 5, 10, 7, 12, 12, 5, 7, 13, 10, 7, 11, 7, 570295, 11, 8, 9, 11, 6, 3877076, 10, 9, 11, 9, 6, 11, 12, 12, 10, 10, 14, 9, 9, 8, 15, 9, 9, 13, 5, 10, 16, 7, 10, 11, 8, 9, 6, 10, 14, 15, 8, 11, 8, 8, 14, 10, 9, 6, 13, 6, 13, 14, 7, 11, 11, 9, 12, 3, 4247384, 10, 14, 15, 9, 14, 3, 9, 10, 7, 14, 15, 13, 16, 14, 11, 11, 13, 9, 5, 10, 7, 5, 8, 11, 10, 12, 10, 11, 11, 7, 12, 9, 9, 8, 13, 13, 9, 15, 10, 5, 9, 9, 2, 13, 9, 11, 11, 11, 8, 8, 11, 11, 7, 12, 34499840, 11, 15, 8, 7, 8, 7, 6, 13, 5, 5, 9, 9, 15, 13, 10, 11, 11, 13, 15, 13, 12, 11, 14, 21003, 11, 10, 1427, 8, 11, 7, 11, 7, 9, 12, 12, 12, 9, 9, 7, 9, 12, 9, 6, 14, 8, 15, 11, 7, 10, 10, 5, 13, 11, 11, 10, 8, 13, 10, 8, 12, 9, 11, 10, 10, 5, 8, 11, 10, 12, 10, 5, 7, 11, 11, 225190, 84981714, 14, 7809277, 11, 11, 7, 7, 10, 11, 11, 10, 7, 7, 1017693, 9, 8, 12, 2, 7, 13, 8, 12, 10, 8, 3, 8, 11, 10, 11, 8, 6, 10, 11, 11, 8, 11, 7, 9, 10, 9, 7310, 6, 8, 12, 9, 9, 8, 9, 6, 13, 8, 10, 8, 9, 9, 9, 7, 11, 12, 11, 7, 7, 12, 13, 8, 13, 7, 277671, 6, 11, 9, 14, 5, 8, 11, 132403, 10, 9, 8, 8, 11, 12, 10, 10, 7, 11, 9, 10, 6, 9, 10, 13, 12, 9, 5, 7, 8, 8, 8, 7, 11, 8, 8, 11, 10, 10, 8, 6, 12, 9, 9, 8, 7, 7, 1557, 6, 5, 13}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 8, 6, 7, 9, 10, 5, 11, 10, 5, 5, 8, 13, 15, 9, 12, 13, 7, 6, 9, 6, 3, 7, 9, 11, 6, 9, 9, 6, 14, 6, 8, 10, 8, 8, 6, 10, 13, 11, 7, 13, 9, 8, 7, 9, 12, 7, 8, 9, 7, 8, 12, 9, 7, 11, 4, 12, 11, 6, 8, 13, 6, 9, 11, 11, 7, 6, 7, 7, 11, 9, 9, 7, 14, 5, 12, 8, 6, 7, 10, 6, 7, 9, 6, 12, 8, 8, 11, 9, 10, 8, 10, 8, 10, 13, 8, 6, 5, 12, 8, 7, 9, 5, 9, 10, 7, 9, 9, 10, 7, 9, 9, 10, 8, 10, 9, 10, 7, 8, 6, 7, 7, 12, 13349, 10, 12, 8, 13, 10, 5, 9, 7, 5, 9, 7, 6, 11, 8, 9, 13, 12, 9, 7, 9, 12, 5, 12, 5, 7, 9, 5, 9, 5, 5, 7, 12, 12, 5, 9, 4, 7, 14, 7, 12, 5, 11, 9, 7, 7, 11, 8, 8, 10, 11, 10, 10, 9, 7, 13, 8, 10, 8, 15, 5, 6, 7, 12, 10, 8, 13, 7, 7, 9, 5, 11, 8, 10, 13, 9, 13, 10, 13, 10, 6, 8, 11, 6, 9, 12, 12, 6, 10, 9, 9, 8, 9, 10, 8, 9, 12, 6, 11, 10, 9, 7, 10, 3, 10, 8, 12, 9, 8, 7, 7, 8, 8, 12, 7, 13, 9, 5, 8, 14, 13, 8, 8, 6, 13, 9, 13, 5, 9, 9, 7, 10, 7, 11, 8, 8, 7, 16, 12, 9, 10, 9, 11, 10, 12, 10, 3, 12, 8, 8, 7, 9, 8, 6, 149453437, 12, 6, 13, 8, 11, 10, 8, 8, 12, 8, 10, 8, 8, 7, 8, 6, 10, 10, 11, 5, 7, 6, 4, 12, 10, 9, 12, 7, 13, 11, 12, 8, 10, 8, 7, 12, 11, 5, 11, 9, 7, 5, 11, 9, 10, 15, 11, 11, 11, 13, 7, 9, 9, 13, 9, 11, 11, 7, 6, 6, 6, 8, 8, 10, 10, 9, 8, 10, 8, 8, 13, 11, 15, 13, 10, 6, 10, 10, 9, 9, 12, 6, 6, 9, 5, 4, 9, 6, 10, 12, 7, 5, 9, 6, 7, 11, 7, 10, 9, 12, 10, 8, 11, 7, 13, 9, 9, 6, 9, 8, 7, 10, 6, 4, 15, 8, 12, 8, 7, 13, 5, 7, 12, 6, 8, 13, 6, 5, 11, 9, 10, 9, 9, 6, 8, 5, 9, 9, 12, 8, 11, 8, 11, 5, 11, 7, 7, 9, 11, 9, 8, 6, 9, 14, 9, 6, 9, 12, 6, 11, 12, 12, 9, 8, 4, 12, 9, 9, 4, 7, 7, 12, 14, 9, 12, 6, 7, 6, 5, 11, 8, 10, 10, 8, 5, 8, 10, 11, 11, 12, 4, 8, 6, 6, 382421525, 10, 5, 6, 13, 10, 8, 6, 9, 10, 13, 7, 6, 13, 4, 4, 6, 9, 8, 11, 9, 7, 9, 11, 13, 6, 8, 6, 10, 12, 11, 7, 7, 7, 6, 6, 9, 7, 6, 9, 13, 10, 14, 8, 8, 7, 6, 7, 8, 6, 10, 11, 11, 7, 12, 7, 7, 11, 8, 8, 13, 8, 5, 9, 10, 6, 9, 11, 9, 9, 9, 11, 11, 12, 16, 8, 12, 6, 5, 6, 12, 6, 12, 11, 8, 10, 5, 8, 8, 7, 12, 10, 5, 14, 6, 10, 12, 11, 5, 6, 8, 11, 5, 8, 11, 8, 11, 8, 8, 9, 9, 9, 9, 13, 3, 10, 6, 9, 7, 6, 9, 10, 10, 13, 8, 8, 8, 10, 9, 12, 13, 11, 7, 11, 7, 9, 9, 8, 9, 16, 12, 12, 14, 9, 5, 6, 8, 10, 7, 8, 11, 7, 9, 11, 10, 9, 7, 4, 5, 6, 6, 11, 7, 9, 9, 12, 12, 5, 5, 8, 8, 11, 11, 16, 6, 9, 9, 6, 11, 6, 10, 12, 7, 6, 8, 14, 6, 8, 8, 10, 9, 9, 10, 9, 10, 7, 9, 8, 11, 9, 10, 11, 12, 8, 8, 8, 7, 5, 10, 9, 11, 12, 8, 10, 6, 13, 6, 11, 11, 5, 12, 9, 11, 5, 8, 6, 8, 5, 8, 15, 12, 9, 11, 12, 7, 14, 10, 12, 9, 8, 6, 8, 11, 9, 5, 12, 9, 12, 12, 11, 9, 7, 9, 7, 12, 9, 6, 6, 7, 6, 8, 7, 7, 12, 9, 4, 7, 7, 7, 13, 12, 7, 11, 6, 6, 4, 10, 7, 8, 9, 8, 10, 6, 9, 11, 9, 8, 10, 6, 8, 5, 8, 14, 10, 8, 10, 8, 7, 11, 7, 12, 10, 13, 10, 4, 6, 5, 12, 10, 14, 13, 12, 8, 7, 9, 12, 9, 12, 11, 11, 7, 12, 9, 7, 15, 8, 7, 13, 5, 6, 5, 5, 7, 8, 7, 9, 7, 7, 12, 8, 7, 9, 6, 5, 11, 6, 9, 13, 16, 11, 11, 5, 9, 5, 12, 9, 10, 10, 8, 6, 7, 10, 9, 7, 8, 3, 5, 8, 10, 11, 8, 5, 6, 8, 7, 11, 11, 6, 9, 10, 10, 12, 6, 6, 6, 7, 12, 6, 9, 7, 7, 13, 7, 12, 7, 9, 14, 12, 12, 3, 7, 10, 7, 12, 6, 13, 7, 9, 7, 10, 10, 9, 12, 8, 9, 10, 11, 6, 5, 9, 14, 12, 6, 9, 7, 11, 7, 7, 7, 8, 8, 5524, 7, 12, 10, 9, 14, 13, 3, 9, 6, 12, 6, 6, 9, 9, 10, 13, 7, 7, 9, 9, 7, 11, 10, 13, 14, 9, 8, 5, 11, 7, 6, 9, 9, 10, 8, 9, 9, 13, 9, 5, 7, 9, 16, 9, 9, 13, 7, 12, 7, 13, 9, 9, 6, 6, 7, 11, 11, 10, 7, 5, 12, 5, 8, 10, 8, 14, 6, 11, 11, 10, 8, 13, 6, 7, 3, 3, 9, 8, 11, 9, 11, 9, 5, 10, 6}

Returns: {-1 }
{13, 11, 10, 13, 10, 11, 13, 8, 7, 7, 7, 7, 194433290, 6, 6, 9, 10, 5, 15, 11, 6, 7, 13, 10, 9, 13, 9, 11, 9, 9, 8, 9, 9, 8, 6, 6, 9, 10, 10, 10, 8, 6, 10, 7, 8, 7, 11, 6, 6, 12, 6, 695804, 11, 11, 11, 9, 10, 7, 6, 13, 10, 10, 7, 11, 11, 9, 8, 7, 4, 6, 11, 5, 10, 10, 6, 13, 8, 10, 10, 9, 10, 13, 7, 8, 9, 7, 10, 7, 8, 7, 10, 7, 10, 6, 5, 9, 13, 6, 11, 5, 9, 9, 11, 9, 13, 8, 7, 8, 7, 10, 10, 8, 8, 9, 2, 9, 9, 10, 6, 7, 9, 10, 7, 7, 10, 6, 8, 6, 9, 13, 11, 9, 7, 7, 13, 11, 12, 6, 6, 8, 9, 9, 12, 8, 6, 8, 9, 8, 8, 6, 8, 10, 10, 7, 7, 5, 10, 7, 10, 6, 7, 6, 9, 9, 9, 11, 8, 230348135, 8, 6, 11, 8, 12, 6, 8, 10, 11, 7, 9, 8, 9, 8, 9, 11, 7, 7, 9, 11, 11, 7, 10, 13, 9, 6, 6, 9, 6, 10, 8, 11, 8, 10, 9, 11, 10, 7, 9, 11, 8, 11, 8, 10, 4, 8, 9, 9, 4, 11, 10, 10, 9, 9, 15, 6, 9, 8, 8, 10, 10, 4, 7, 8, 9, 7, 9, 11, 10, 10, 4, 9, 9, 10, 12, 7, 8, 10, 7, 10, 12, 9, 7, 6, 10, 8, 10, 5, 11, 8, 9, 6, 10, 10, 9, 10, 12, 10, 10, 6, 12, 7, 9, 8, 6, 9, 2, 5, 13, 11, 12, 7, 12, 11, 9, 10, 10, 8, 11, 8, 9, 7, 12, 12, 3, 10, 8, 10, 8, 10, 11, 12, 7, 8, 11, 8, 9, 11, 10, 6, 8, 9, 7, 7, 5, 10, 12, 7, 6, 11, 8, 9, 6, 8, 10, 7, 7, 9, 7, 11, 7, 74308, 9, 12, 12, 6, 8, 11, 8, 8, 11, 4, 7, 7, 7, 7, 8, 12, 11, 6, 6, 9, 4, 10, 10, 5, 9, 9, 7, 9, 6, 11, 11, 6, 7, 11, 9, 7, 9, 12, 6, 12, 9, 9, 7, 9, 10, 8, 6, 11, 10, 10, 10, 7, 6, 10, 6, 11, 10, 5, 6, 8, 12, 11, 7, 9, 7, 10, 13, 8, 5, 10, 11, 7, 9, 10, 9, 15, 8, 11, 6, 8, 7, 7, 8, 10, 7, 6, 9, 7, 8, 9, 9, 6, 10, 5, 11, 7, 11, 7, 10, 9, 10, 8, 13, 5, 11, 8, 11, 8, 8, 12, 9, 7, 7, 7, 6, 7, 12, 6, 8, 7, 7, 5, 9, 6, 9, 4, 9, 10, 9, 10, 7, 6, 10, 9, 9, 14, 9, 8, 8, 10, 8, 7, 6, 8, 6, 6, 9, 7, 8, 10, 6, 8, 8, 10, 8, 9, 9, 10, 8, 12, 10, 5, 6, 13, 11, 8, 10, 11, 9, 7, 10, 9, 9, 8, 10, 11, 10, 5, 9, 6, 6, 6, 10, 12, 12, 7, 7, 9, 10, 8, 10, 4, 8, 6, 13, 10, 9, 8, 8, 8, 13, 7, 6, 10, 6, 9, 11, 7, 12, 8, 6, 14, 7, 11, 11, 4, 11, 12, 9, 8, 5, 4, 7, 5, 9, 14, 9, 8, 9, 7, 9, 7, 9, 8, 10, 11, 9, 12, 8, 5, 11, 12, 6, 7, 9, 6, 8, 14297, 7, 8, 6, 5, 5, 12, 7, 9, 9, 5, 9, 14, 11, 10, 7, 9, 6, 8, 11, 10, 12, 9, 9, 11, 9, 8, 7, 10, 11, 11, 10, 13, 7, 6, 8, 9, 9, 8, 8, 10, 12, 9, 6, 7, 9, 8, 9, 6, 6, 9, 9, 9, 7, 10, 7, 9, 12, 9, 5, 11, 8, 8, 10, 5, 11, 8, 8, 7, 7, 9, 13, 5, 12, 9, 7, 8, 10, 8, 8, 9, 7, 6, 9, 6, 4, 8, 7, 11, 9, 9, 7, 10, 5, 8, 10, 9, 6, 9, 9, 8, 12, 8, 8, 9, 11, 8, 9, 9, 13, 6, 13, 11, 10, 13, 10, 9, 11, 12, 6, 8, 9, 6, 7, 7, 4, 10, 10, 14, 9, 8, 7, 10, 6, 9, 13, 9, 11, 9, 8, 9, 9, 6, 10, 7, 7, 11, 12, 11, 5, 12, 7, 11, 13, 9, 10, 7, 5, 10, 10, 6, 8, 10, 7, 10, 7, 8, 8, 7, 10, 13, 9, 7, 8, 10, 11, 9, 10, 5, 11, 10, 6, 6, 10, 7, 10, 11, 6, 13, 11, 5, 8, 6, 10, 7, 9, 10, 13, 4, 9, 6, 9, 11, 8, 7, 7, 8, 8, 6, 10, 7, 9, 208017, 7, 7, 4, 10, 13, 10, 10, 8, 8, 12, 8, 12, 7, 10, 11, 5, 6, 11, 10, 7, 11, 11, 10, 7, 10, 6, 10, 11, 7, 13, 9, 7, 8, 11, 11, 13, 12, 7, 10, 12, 9, 7, 7, 7, 12, 10, 6, 11, 10, 10, 8, 8, 9, 10, 7, 10, 10, 2, 6, 9, 12, 6, 8, 9, 12, 6, 12, 9, 8, 9, 7, 7, 10, 11, 8, 9, 5, 8, 11, 7, 9, 6, 13, 6, 11, 11, 10, 12, 6, 8, 10, 9, 6, 7, 6, 3, 10, 11, 6, 10, 6, 7, 12, 6, 11, 9, 10, 10, 8, 43773873, 5, 8, 8, 10, 7, 11, 10, 9, 8, 10, 6, 7, 9, 13, 7, 9, 11, 8, 8, 11, 6, 7, 8, 7, 7, 10, 11, 7, 7, 12, 5, 5, 9, 7, 12, 5, 10, 11, 8, 5, 10, 8, 11, 11, 6, 11, 11, 12, 6, 9, 9, 6, 9, 6, 8, 9, 9, 9, 11, 6, 7, 5, 7, 5, 11, 10}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{5, 11, 9, 13, 6, 15, 4, 6, 8, 10, 7, 8, 9, 9, 11, 13, 7, 12, 5, 12, 13, 5, 13, 6, 9, 11, 6, 7, 6, 6, 6, 14, 7, 5, 8, 7, 10, 11, 6, 11, 7, 9, 8, 9, 13, 10, 13, 14, 10, 9, 12, 9, 13, 11, 7, 10, 6, 6, 3246, 6, 10, 7, 7, 7, 7, 11, 8, 5, 7, 9, 9, 8, 9, 8, 9, 9, 12, 5, 8, 7, 8, 13, 12, 4, 7, 9, 7, 6, 7, 9, 4, 5, 9, 6, 15, 6, 6, 8, 8, 6, 1558, 8, 8, 8, 13, 8, 7, 5, 5, 8, 6, 9, 5, 7, 5, 7, 8, 9, 10, 13, 9, 10, 14, 14, 10, 8, 12, 5, 4, 6, 7, 9, 12, 13, 9, 10, 8, 8, 12, 13, 8, 9, 9, 9, 7, 13, 11, 8, 9, 10, 8, 9, 5, 8, 13, 8, 7, 13, 8, 8, 12, 14, 8, 8, 7, 7, 7, 5591, 5, 7, 10, 10, 10, 10, 138073, 9, 13, 8, 13, 6, 9, 10, 9, 11, 8, 8, 10, 5, 7, 7, 11, 10, 6, 9, 12, 12, 8, 14, 5, 805101, 9, 9, 9, 7, 12, 5, 12, 9, 5, 11, 14, 7, 10, 7, 8, 9, 8, 14, 10, 9, 9, 300015, 9, 15, 230058, 8, 12, 8, 11, 12, 7, 11, 7, 4, 4, 7, 11, 6, 8, 4, 9, 4, 8, 11, 12, 9, 14, 12, 8, 6, 14, 12, 9, 11, 4, 6, 6, 13, 9, 9, 6, 14, 13, 6, 15208, 9, 11, 10, 12, 8, 2068, 12, 5, 8, 10, 8, 12, 7, 8, 11, 7, 12, 8, 10, 15, 8, 11, 10, 14, 9, 9, 11, 4, 11, 13, 7, 9, 11, 7, 9, 7, 5, 7, 9, 13, 9, 13, 8, 12, 9, 6, 9, 8, 10, 9, 13, 11, 5, 6, 7, 9, 10, 10, 10, 8, 6, 8, 6, 6, 15, 11, 11, 7, 9, 8, 6, 10, 8, 8, 7, 6, 11, 5737928, 20283, 9, 9, 9, 8, 13, 6, 9, 5, 4, 276362612, 8, 9, 9, 9, 7, 8, 7, 11, 6, 5, 5, 7, 10, 12, 7, 7, 7, 8, 8, 7, 12, 14, 9, 10, 10, 14, 5, 5, 7, 11, 7, 12, 8, 7, 6, 9, 8, 9, 12, 10, 8, 9, 499526, 13, 13, 5, 6, 8, 12, 5, 10, 13, 13, 449354917, 9, 12, 7, 13, 9, 11, 9, 7, 5, 6, 5, 13, 11, 6, 6, 358116107, 9, 13, 8, 5, 8, 11, 12, 5, 12, 10, 4, 7, 8, 6, 7, 6107, 8, 7, 7, 7, 9, 8, 1200, 8, 13, 7, 13, 5, 9, 13, 5, 14, 14, 8, 3, 8, 6, 5, 4, 9, 7, 12, 11, 5, 7, 10, 10, 8, 6, 7, 10, 6, 12, 9, 11, 10, 7, 8, 47645, 10, 14, 13, 5, 8, 7, 9, 5, 12, 7, 12, 8, 8, 11, 10, 4, 14, 6, 5, 9, 4, 13, 9, 13, 14, 2330, 8, 10, 5, 7, 10, 8, 8, 10, 8, 8, 9, 8, 14, 6, 7, 8, 9, 5283592, 8, 6, 7, 9, 12, 9, 11, 13, 8, 12, 7, 8, 8, 6, 7, 6, 8, 10, 6, 9, 11, 11, 9, 7, 9, 5, 12, 7, 8, 8, 6, 11, 4895, 5, 10, 11, 9, 9, 7, 6, 2, 14, 9, 7, 14, 8, 14, 3, 9, 11, 7, 8, 10, 13, 5, 10, 7, 11, 8, 13, 9, 9, 13, 6, 14, 7, 7, 9, 10, 11, 14, 8, 7, 6, 10, 11, 12, 6, 12, 9, 13, 7, 4, 13, 9, 14, 11, 8, 9, 6, 7, 5239, 4, 9, 12, 15, 11, 6, 11, 9, 12, 8, 5, 7, 11, 10, 10, 10, 7, 13, 10, 10, 8, 9, 7, 15, 8, 36678165, 14, 7, 12, 6, 10, 8, 5, 9, 10, 9, 14, 13, 6, 11, 9, 13, 11, 8, 6, 8, 9, 5, 7, 8, 8, 9, 10, 8, 8, 7, 13, 7, 10, 9, 9, 11, 10, 5860, 9, 12, 7, 8, 10, 7, 7, 7336, 14, 9, 9, 8, 12, 7, 8, 9, 8, 10, 11, 14, 10, 8, 9, 12, 12, 8, 9, 12, 8, 9, 10, 9, 1718348, 8, 7, 8, 9, 8, 4, 10, 8, 7, 9, 13, 5, 12, 12, 6, 7, 13, 13, 13, 11, 5, 9, 12, 9, 10, 8, 87426, 6, 10, 9, 10, 7, 6, 8, 10, 12, 8, 5, 12, 6, 12, 14, 6, 12, 9, 6, 5, 12, 12, 6, 7, 10, 7, 8, 22767, 7, 12, 9, 4, 6, 10, 12, 12, 5, 7, 6, 11, 10, 9, 9, 10, 9, 6, 6, 8, 11, 10, 9, 1441036, 9, 6, 10, 7, 13, 12, 8, 7, 209717, 6, 5, 4, 12, 4, 14, 7, 7, 9, 6, 4, 8, 11, 7, 13, 9, 10, 8, 5, 9, 11, 9, 8, 14, 10, 6, 6, 6, 14, 6, 14552, 4, 12, 5, 7, 7, 11, 9, 12, 4, 7, 11, 12, 6, 9, 9, 13, 8, 12, 12, 6, 10, 6, 7, 13, 7, 9, 14, 12, 10, 9, 13, 9, 8, 6, 8, 10, 6, 4, 9, 12, 11, 7, 8, 12, 8, 13, 13, 12, 11, 12, 14, 15, 5, 14, 6, 7, 6, 6, 6, 4, 9, 8, 11, 9, 5, 10, 13, 5, 8, 5, 5, 13, 8, 12, 31235, 124294, 13, 14, 11, 10, 7, 11, 4, 10, 8, 13, 6, 6, 7, 7, 12, 7, 9, 8, 9, 11, 10, 9, 12, 12, 15, 6, 9, 8, 9, 10, 7, 10, 12, 7, 13, 7, 5, 11, 12, 5, 8, 11, 9, 14, 7, 6, 8, 6, 7, 9, 9, 5, 14, 10, 8, 10, 14, 9, 8, 12, 8, 11, 8, 11, 7, 12, 13, 9, 5, 7, 8, 14, 9, 12, 13, 10, 5, 9, 11, 9, 6, 7, 6, 14, 10, 14, 10, 8, 14}

Returns: {1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{13, 6, 10, 6, 8, 11, 10, 12, 3, 11, 6, 13, 7, 12, 8, 7, 9, 11, 14, 6, 8, 13, 6, 8, 10, 11, 9, 7, 10, 11, 7, 4, 6, 12, 11, 5, 11, 12, 10, 3, 13, 10, 9, 12, 11, 13, 9, 12, 15, 10, 9, 8, 4, 11, 6, 9, 14, 13, 8, 12, 5, 6, 13, 6, 13, 11, 7, 7, 14, 10, 4, 10, 5, 9, 7, 5, 9, 10, 9, 9, 14, 11, 7, 8, 11, 8, 12, 10, 14, 12, 7, 8, 14, 13, 10, 7, 10, 12, 12, 7, 8, 13, 9, 10, 9, 7, 12, 6, 9, 12, 9, 10, 9, 11, 8, 11, 5, 13, 12, 8, 14, 7, 13, 7, 7, 9, 7, 7, 13, 12, 8, 9, 13, 8, 11, 10, 7, 10, 15, 11, 8, 15, 8, 11, 7, 9, 9, 13, 8, 15, 9, 14, 11, 7, 9, 9, 8, 11, 11, 7, 6, 10, 10, 10, 10, 9, 10, 9, 6, 8, 10, 11, 9, 12, 8, 8, 10, 14, 10, 12, 8, 8, 8, 8, 10, 9, 7, 8, 10, 7, 6, 9, 7, 8, 13, 10, 9, 10, 10, 10, 10, 6, 14, 10, 12, 10, 11, 12, 14, 8, 7, 13, 13, 8, 9, 6, 9, 13, 12, 7, 12, 7, 12, 7, 5, 10, 9, 9, 5, 10, 14, 4, 5, 7, 8, 8, 13, 7, 8, 13, 8, 10, 9, 9, 9, 12, 12, 9, 7, 10, 7, 11, 7, 10, 7, 10, 12, 11, 8, 8, 8, 8, 7, 10, 13, 13, 12, 14, 8, 7, 5, 5, 10, 12, 6, 6, 4, 11, 12, 11, 8, 11, 9, 10, 12, 9, 10, 14, 8, 10, 5, 9, 12, 7, 12, 12, 14, 14, 9, 12, 11, 11, 9, 10, 10, 11, 12, 14, 12, 7, 8, 10, 12, 11, 9, 10, 11, 10, 9, 13, 10, 9, 10, 11, 6, 13, 10, 12, 4, 10, 12, 15, 12, 10, 7, 12, 9, 10, 6, 10, 10, 12, 14, 12, 9, 10, 8, 10, 6, 8, 12, 10, 10, 14, 10, 9, 11, 10, 7, 9, 13, 9, 6, 6, 6, 13, 5, 11, 5, 12, 11, 8, 12, 6, 7, 9, 11, 11, 9, 11, 3, 14, 7, 14, 11, 11, 8, 8, 11, 6, 12, 8, 7, 11, 10, 8, 9, 9, 12, 13, 5, 12, 14, 15, 12, 7, 13, 12, 8, 12, 11, 10, 8, 11, 10, 13, 11, 13, 5, 11, 12, 11, 15, 5, 12, 12, 13, 9, 12, 8, 10, 4, 9, 13, 7, 10, 12, 10, 9, 12, 13, 11, 14, 14, 12, 7, 6, 11, 10, 10, 7, 11, 10, 11, 13, 14, 13, 8, 17, 10, 9, 10, 7, 6, 13, 11, 9, 5, 14, 11, 7, 8, 6, 8, 10, 7, 12, 11, 5, 10, 9, 8, 10, 10, 11, 12, 15, 14, 9, 8, 11, 9, 9, 10, 8, 12, 12, 12, 8, 14, 10, 7, 9, 8, 11, 8, 10, 10, 7, 9, 11, 11, 10, 7, 11, 6, 10, 14, 7, 9, 14, 10, 11, 12, 12, 12, 9, 8, 14, 9, 8, 7, 14, 8, 8, 8, 13, 12, 12, 7, 9, 14, 9, 11, 9, 7, 9, 5, 8, 11, 10, 11, 9, 11, 9, 9, 13, 13, 6, 14, 8, 9, 12, 14, 7, 9, 7, 7, 11, 7, 12, 9, 13, 9, 9, 9, 12, 4, 6, 8, 11, 3, 9, 8, 6, 8, 14, 11, 11, 9, 9, 12, 11, 10, 11, 10, 13, 10, 12, 10, 5, 10, 10, 7, 11, 11, 11, 8, 9, 9, 6, 10, 13, 12, 12, 6, 8, 12, 11, 9, 9, 7, 11, 16, 9, 10, 7, 13, 4532046, 8, 13, 9, 8, 9, 14, 12, 8, 9, 9, 11, 11, 9, 8, 12, 13, 12, 9, 6, 11, 14, 10, 10, 10, 9, 9, 8, 6, 7, 6, 11, 7, 7, 7, 6, 12, 10, 5, 12, 9, 5, 14, 8, 8, 14, 12, 7, 12, 15, 7, 9, 12, 10, 14, 14, 7, 11, 10, 6, 3, 9, 9, 10, 2, 10, 7, 12, 14, 8, 6, 11, 9, 6, 13, 4, 8, 13, 11, 6, 11, 10, 9, 9, 11, 7, 9, 6, 5, 9, 13, 5, 11, 12, 13, 12, 14, 11, 12, 8, 13, 11, 11, 11, 6, 10, 11, 5, 10, 12, 12, 9, 5, 12, 8, 11, 8, 10, 9, 6, 10, 8, 13, 9, 7, 10, 4, 10, 12, 11, 9, 10, 14, 6, 11, 9, 12, 8, 10, 9, 15, 12, 6, 7, 8, 14, 9, 11, 8, 5, 8, 11, 11, 10, 8, 6, 12, 10, 8, 8, 13, 11, 11, 9, 7, 15, 9, 9, 9, 8, 9, 7, 7, 10, 9, 10, 5, 8, 7, 12, 9, 14, 10, 12, 9, 9, 12, 10, 7, 8, 13, 15, 9, 10, 10, 9, 6, 8, 10, 10, 15, 10, 10, 6, 13, 11, 15, 7, 9, 5, 12, 11, 16, 10, 11, 7, 11, 8, 6, 7, 11, 9, 7, 10, 14, 12, 9, 5, 11, 10, 4, 11, 13, 8, 17, 12, 10, 8, 10, 8, 9, 14, 9, 11, 11, 7, 10, 9, 12, 9, 7, 14, 12, 6, 10, 11, 11, 14, 8, 10, 9, 10, 14, 6, 15, 7, 8, 11, 9, 11, 12, 11, 7, 14, 8, 9, 8, 7, 7, 9, 9, 13, 12, 13, 7, 10, 12, 14, 11, 10, 8, 12, 12, 3, 11, 10, 10, 8, 3, 7, 2, 12, 11, 14, 11, 10, 8, 10, 10, 12, 10, 15, 10, 10, 10, 12, 6, 12, 12, 10, 12, 12, 11, 8, 7, 13, 10, 11, 12, 12, 13, 13, 12, 13, 12, 11, 16, 8, 12, 7, 12, 12, 7, 13, 11, 10, 14, 11, 10, 12, 12, 13, 14, 12, 13, 17, 12, 11, 7, 12, 9, 6, 8, 13, 2, 8, 6, 11, 10, 10, 9, 10}

Returns: {-1 }
{5, 6, 5, 9, 12, 9, 9, 8, 5, 8, 11, 7, 7, 14, 8, 12, 9, 5, 10, 13, 10, 10, 9, 8, 11, 9, 6, 11, 11, 12, 6, 6, 9, 11, 8, 10, 6, 11, 13, 9, 5, 9, 8, 9, 10, 9, 6, 7, 14, 7, 5, 6, 8, 9, 5, 11, 7, 8, 11, 9, 5, 11, 6, 7, 10, 7, 8, 8, 6, 8, 9, 6, 7, 11, 10, 11, 7, 9, 6, 10, 11, 9, 10, 11, 5, 9, 11, 10, 11, 14, 9, 6, 6, 7, 14, 7, 10, 8, 13, 10, 8, 9, 8, 9, 8, 7, 8, 7, 8, 8, 8, 4, 13, 10, 9, 6, 10, 10, 15, 6, 7, 5, 9, 12, 8, 10, 8, 9, 8, 9, 8, 8, 8, 11, 12, 12, 7, 7, 8, 4, 6, 7, 8, 11, 3, 6, 7, 9, 8, 8, 9, 6, 6, 16, 8, 8, 11, 11, 9, 9, 10, 5, 9, 10, 10, 7, 9, 6, 8, 9, 10, 8, 11, 9, 9, 10, 9, 8, 10, 6, 9, 9, 9, 9, 11, 9, 6, 8, 8, 7, 10, 10, 11, 10, 8, 6, 7, 10, 8, 11, 9, 11, 10, 13, 7, 11, 6, 10, 6, 10, 8, 7, 6, 12, 9, 8, 10, 10, 13, 14, 9, 5, 11, 12, 9, 13, 9, 7, 11, 10, 10, 9, 11, 7, 5, 7, 12, 10, 13, 9, 11, 10, 12, 8, 10, 10, 7, 13, 12, 6, 8, 8, 11, 10, 7, 6, 12, 7, 8, 9, 6, 12, 6, 8, 8, 8, 6, 6, 7, 11, 12, 7, 12, 10, 9, 10, 13, 7, 9, 9, 9, 3, 10, 7, 10, 5, 9, 12, 8, 7, 11, 7, 7, 10, 13, 5, 8, 11, 7, 12, 9, 11, 8, 6, 9, 10, 9, 8, 8, 11, 10, 10, 6, 7, 5, 11, 8, 7, 10, 7, 12, 12, 12, 7, 8, 8, 13, 11, 7, 8, 11, 9, 9, 11, 10, 10, 5, 5, 7, 5, 13, 11, 9, 8, 7, 10, 6, 10, 8, 9, 9, 8, 10, 10, 14, 12, 11, 12, 7, 11, 13, 11, 10, 9, 12, 10, 6, 7, 8, 13, 7, 11, 11, 7, 12, 11, 8, 12, 10, 6, 8, 6, 8, 7, 14, 6, 7, 10, 5, 6, 9, 10, 13, 8, 6, 11, 5, 10, 7, 10, 11, 9, 14, 16230, 11, 13, 13, 9, 7, 9, 9, 6, 11, 9, 13, 11, 8, 12, 13, 6, 10, 6, 9, 6, 8, 10, 7, 11, 10, 4, 9, 8, 8, 10, 6, 9, 6, 11, 8, 12, 6, 6, 7, 7, 10, 6, 13, 10, 10, 9, 12, 10, 10, 6, 8, 9, 13, 10, 10, 6, 9, 10, 11, 13, 3, 6, 10, 8, 13, 6, 8, 11, 10, 5, 5, 9, 9, 13, 12, 10, 10, 4, 9, 8, 9, 9, 10, 5, 12, 14, 7, 11, 10, 10, 10, 7, 6, 8, 10, 10, 6, 10, 6, 7, 8, 5, 11, 9, 8, 8, 11, 8, 11, 8, 9, 10, 7, 11, 8, 13, 7, 6, 5, 6, 7, 8, 8, 11, 7, 10, 5, 9, 13, 10, 11, 7, 9, 7, 6, 16, 10, 10, 8, 10, 9, 8, 11, 7, 8, 8, 11, 7, 16, 13, 10, 13, 16, 14, 8, 11, 13, 13, 10, 8, 10, 10, 12, 13, 7, 9, 11, 2, 6, 13, 12, 8, 4, 16, 7, 9, 11, 8, 6, 13, 7, 11, 4, 8, 9, 9, 5, 6, 6, 9, 12, 5, 12, 8, 10, 10, 7, 10, 7, 6, 10, 10, 10, 10, 9, 8, 8, 8, 11, 11, 10, 7, 11, 8, 9, 10, 11, 13, 6, 9, 6, 10, 11, 11, 9, 9, 14, 8, 7, 6, 7, 11, 6, 10, 8, 9, 12, 8, 6, 7, 9, 11, 13, 10, 8, 6, 11, 7, 10, 7, 9, 9, 13, 10, 8, 10, 11, 5, 4, 7, 5, 12, 14, 5, 10, 9, 4, 7, 10, 12, 3, 6, 7, 10, 11, 8, 11, 11, 10, 7, 11, 8, 13, 13, 4, 9, 10, 3, 9, 8, 6, 8, 3, 9, 8, 10, 8, 11, 6, 13, 9, 7, 4, 7, 8, 13, 9, 11, 9, 6, 8, 12, 8, 9, 9, 6, 5, 11, 12, 9, 9, 11, 10, 5, 7, 6, 6, 8, 10, 12, 11, 6, 10, 6, 11, 11, 10, 9, 5, 13, 7, 9, 9, 11, 11, 11, 11, 6, 10, 9, 10, 7, 10, 9, 7, 11, 5, 10, 7, 8, 6, 8, 10, 8, 10, 5, 4, 10, 10, 11, 13, 7, 10, 16, 6, 9, 13, 6, 12, 10, 9, 7, 6, 11, 5, 7, 10, 9, 11, 7, 11, 13, 10, 10, 6, 12, 5, 10, 10, 9, 10, 12, 8, 10, 8, 6, 9, 8, 11, 6, 10, 9, 9, 9, 14, 10, 9, 7, 9, 9, 10, 10, 10, 6, 4, 6, 11, 10, 6, 11, 9, 10, 22794199, 6, 14, 10, 7, 5, 11, 7, 14, 10, 11, 13, 6081270, 12, 7, 13, 9, 11, 6, 13, 9, 7, 10, 6, 5, 10, 10, 9, 5, 6, 10, 10, 9, 3, 7, 8, 8, 10, 13, 8, 9, 7, 9, 9, 9, 8, 13, 8, 14, 9, 11, 4, 10, 10, 10, 10, 10, 8, 9, 5, 11, 8, 8, 9, 10, 12, 5, 11, 10, 9, 7, 10, 8, 7, 5, 6, 9, 5, 10, 9, 8, 12, 8, 6, 7, 8, 12, 8, 12, 7, 11, 9, 5, 9, 9, 12, 9, 10, 10, 8, 13, 9, 9, 9, 7, 9, 9, 10, 11, 12, 6, 5, 9, 9, 9, 12, 7, 11, 14, 10, 7, 7, 8, 7, 9, 9, 10, 6, 8, 8, 9, 8, 9, 9, 10, 11, 8, 12, 9, 12, 11, 12, 8, 10, 4, 3, 10, 10, 8, 8, 12, 10, 10, 9, 9, 12, 5, 11}

Returns: {1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{11, 8, 8, 7, 9, 7, 6, 8, 8, 11, 5, 7, 9, 8, 6, 9, 8, 6, 6, 11, 9, 7, 6, 9, 12, 9, 2, 7, 1459, 10, 7, 10, 7, 8, 12, 10, 11, 8, 7, 10, 10, 10, 10, 4, 11, 9, 8, 8, 9, 7, 8, 8, 8, 8, 7, 7, 9, 9, 9, 8, 7, 10, 6, 6, 11, 6, 8, 13, 5, 8, 9, 7, 7, 10, 9, 6, 8, 7, 13, 11, 9, 8, 10, 7, 8, 10, 8, 9, 7, 9, 8, 15, 14, 10, 8, 5, 11, 3, 10, 7, 9, 7, 12, 11, 9, 6, 8, 8, 11, 7, 7, 6, 7, 9, 9, 13, 8, 9, 4, 14, 8, 10, 9, 9, 6, 5, 10, 8, 10, 10, 9, 10, 10, 8, 9, 8, 9, 9, 10, 8, 8, 8, 6, 9, 6, 12, 10, 7, 6, 8, 12, 5, 10, 12, 7, 6, 9, 12, 9, 10, 13, 9, 9, 12, 14, 12, 97665, 6, 8, 10, 10, 12, 8, 11, 7, 8, 6, 13, 4464957, 8, 7, 10, 8, 8, 10, 15, 7, 8, 6, 6, 8, 4, 10, 9, 5, 9, 8, 12, 6, 6, 10, 7, 12, 10, 8, 11, 11, 15, 10, 6, 6, 9, 13, 7, 7, 10, 10, 9523, 8, 8, 12, 10, 6, 8, 7, 8, 16, 9, 10, 7, 8, 11, 7, 8, 9, 9, 9, 5, 9, 7, 9, 9, 7, 9, 10, 7, 7, 15, 9, 7, 9, 9, 8, 10, 9, 7, 6, 8, 10, 7, 16, 11, 9, 9, 6, 12, 11, 11, 10, 8, 11, 11, 4, 9, 9, 9, 8, 10, 9, 8, 7, 9, 9, 11, 10, 10, 15, 15, 11, 9, 8, 7, 9, 12, 9, 12, 8, 10, 10, 9, 9, 7, 6, 9, 10, 10, 8, 10, 9, 9, 7, 13, 11, 7, 15, 7, 8, 8, 8, 11, 9, 9, 10, 9, 12, 30786297, 8, 8, 8, 11, 7, 7, 8, 8, 11, 10, 9, 8, 8, 8, 13, 7, 11, 13, 11, 14, 14, 6, 10, 10, 8, 7, 10, 7, 8, 15, 12, 10, 9, 8, 8, 9, 9, 12, 9, 7, 10, 9, 11, 8, 10, 9, 7, 13, 8, 13, 10, 10, 10, 14, 10, 7, 13, 12, 10, 10, 13, 10, 9, 10, 7, 15, 9, 6, 7, 6, 7, 8, 10, 11, 12, 9, 6, 9, 9, 6, 6, 13, 5, 9, 9, 6, 7, 9, 9, 11, 7, 11, 11, 5, 7, 9, 13, 8, 6, 9, 11, 7, 12, 11, 8, 7, 4, 6, 9, 8, 7, 8, 6, 7, 7, 6, 13, 8, 11, 8, 10, 6, 12, 8, 8, 9, 6, 14, 8, 7, 10, 9, 7, 9, 11, 8, 8, 13, 10, 10, 10, 10, 1927181, 10, 14, 2, 12, 8, 8, 10, 14, 8, 8, 6, 7, 9, 7, 7, 12, 10, 9, 8, 3, 15, 10, 9, 8, 7, 10, 9, 7, 7792589, 10, 10, 9, 9, 10, 11, 8, 8, 10, 544913, 8, 12, 9, 9, 9, 9, 12, 10, 9, 9, 10, 12, 6, 12, 8, 8, 9, 11, 11, 8, 481996, 10, 8, 7, 8, 12, 8, 6, 11, 10, 8, 10, 6, 10, 6, 6, 8, 6, 10, 10, 11, 13, 5, 8, 7, 14, 10, 9, 8, 12, 11, 8, 8, 10, 11, 10, 8, 10, 9, 5, 5, 6, 154224, 10, 10, 11, 9, 9, 8, 4, 10, 16, 8, 7, 11, 12, 2354, 12, 9, 8, 14, 11, 10, 10, 9, 6, 8, 13, 2, 11, 14, 5, 11, 7, 9, 7, 9, 8, 10, 5, 10, 10, 10, 7, 10, 10, 8, 5, 9, 12, 11, 9, 12, 8, 11, 5, 9, 8, 7, 11, 6, 6, 6, 5, 8, 6, 8, 9, 13, 6, 11, 8, 5, 12, 11, 8, 7, 3589, 11, 8, 9, 7, 10, 9, 9, 16, 11, 8, 7, 12, 10, 9, 10, 12, 12, 12, 10, 12, 9, 9, 8, 8, 10, 12, 9, 10, 5, 6, 9, 7, 10, 8, 8, 10, 12, 10, 12, 11, 14, 8, 9, 8, 8, 8, 6, 8, 9, 10, 8, 12, 10, 4, 8, 10, 6, 14, 8, 13, 12, 12, 8, 4, 8, 8, 12, 9, 10, 8, 8, 4, 8, 10, 6, 8, 11, 10, 12, 9, 8, 10, 10, 9, 6, 5, 5, 3, 9, 15, 11, 6, 10, 13, 12, 8, 11, 9, 9, 6, 15, 15, 11, 9, 9, 20574096, 9, 5, 8, 8, 8, 8, 7, 10, 6, 10, 7, 9, 12, 9, 7, 6, 7, 10, 9, 12, 6, 8, 7, 7, 12, 15, 9, 7, 12, 9, 9, 5, 9, 10, 7, 7, 10, 10, 7, 10, 14, 7, 9, 8, 10, 8, 15, 78932, 11, 4, 8, 6, 11, 10, 12, 8, 9, 6, 11, 6, 8, 12, 4, 9, 10, 5, 10, 9, 8, 8, 6, 8, 16, 10, 10, 6, 11, 14, 11, 5, 7, 7, 11, 11, 13, 9, 9, 8, 9, 8, 9, 7, 11, 9, 8, 12, 9, 11, 9, 9, 8, 9, 9, 13, 15, 15, 9, 11, 9, 8, 7, 9, 11, 10, 6, 9, 6, 9, 6, 10, 7, 6, 10, 3, 9, 11, 7, 9, 9, 11, 8, 12, 8, 8, 10, 7, 8, 9, 8, 11, 11, 11, 7, 9, 8, 13, 10, 10, 12, 6, 6, 10, 8, 15, 9, 8, 12, 8, 16, 6, 9, 12, 9, 6, 9, 12, 10, 13, 12, 8, 10, 7, 7, 7, 15, 9, 7, 9, 79000167, 11, 7, 7, 8, 8, 13, 10, 8, 9, 8, 12, 11, 8, 8, 7, 8, 3, 11, 6, 6, 7, 7, 9, 6, 9, 7, 10, 8, 9, 11, 7, 10, 4, 7, 7, 12, 14, 10, 8, 5, 10, 9, 9, 9, 5, 7, 6, 11, 12, 11, 6, 13, 6, 6, 7, 4, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 8, 6, 8, 17873423, 14, 8, 8, 9, 10, 8, 8, 6, 7, 10, 7, 11, 11, 7, 11, 7, 13, 8, 12, 7, 13, 10, 9, 9, 5, 10, 6, 8, 9, 7, 9, 8, 9, 8, 9, 4, 8, 14, 10, 11, 6, 11, 10, 10, 12, 10, 5, 6, 12, 7, 12, 12, 8, 10, 13, 12, 10, 6, 9, 9, 10, 10, 10, 8, 9, 7, 10, 8, 15, 12, 3, 12, 9, 8, 11, 7, 8, 10, 9, 9, 11, 12, 9, 10, 9, 5, 12, 10, 9, 13, 10, 10, 7, 12, 17, 9, 10, 10, 6, 13, 13, 8, 14, 9, 7, 7, 11, 15, 13, 10, 11, 11, 10, 4, 9, 11, 11, 7, 8, 9, 5, 10, 9, 10, 9, 7, 8, 7, 8, 10, 9, 9, 4, 7, 5, 11, 7, 8, 8, 9, 337260941, 6, 4, 8, 8, 6, 6, 8, 9, 8, 9, 9, 5, 9, 5, 667718, 7, 10, 12, 12, 10, 7, 9, 8, 12, 9, 9, 11, 8, 8, 10, 8, 9, 11, 10, 7, 6, 9, 11, 8, 8, 9, 9, 11, 849128, 8, 4, 14, 9, 7, 10, 9, 11, 7, 11, 8, 16, 9, 9, 9, 10, 13, 10, 7, 10, 14, 12, 10, 12, 9, 10, 7, 8, 9, 5, 13, 10, 9, 7, 10, 11, 8, 17, 10, 10, 10, 7, 7, 11, 8, 9, 7, 7, 15, 8, 6, 7, 9, 7, 7, 15, 7, 9, 10, 10, 9, 9, 9, 5, 7, 8, 9, 11, 9, 6, 11, 11, 8, 8, 12, 12, 10, 7, 11, 9, 7, 12, 2, 11, 9, 7, 5, 6, 10, 122580212, 9, 5, 10, 8, 4, 231761, 5, 12667, 11, 10, 4, 7, 10, 13, 12, 15, 12, 17, 8, 7, 9, 6, 8, 11, 9, 7, 6, 8, 10, 6, 8, 12, 8, 10, 8, 9, 8, 8, 10, 7, 13, 11, 13, 5, 10, 9, 10, 14, 9, 7, 2, 15, 5, 6, 9, 5, 8, 11, 6, 5, 7, 12, 6, 10, 11, 13, 7, 8, 9, 7, 4, 8, 9, 11, 7, 8, 6, 6, 10, 8, 6, 8, 8, 8, 10, 9, 9, 6, 9, 4, 14, 11, 10, 9, 9, 7, 9, 8, 11, 12, 9, 9, 13, 10, 11, 4, 5, 11, 8, 7, 8, 7, 13, 7, 8, 7, 9, 6, 11, 11, 13, 9, 7, 5, 6, 12, 15, 9, 9, 7, 7, 7, 9, 7, 9, 9, 11, 10, 6, 10, 10, 6, 10, 10, 10, 10, 12, 12, 5, 5, 9, 4, 7, 7, 15, 8, 8, 9, 20389, 12, 9, 287886170, 5, 73171614, 7, 8, 10, 11, 7, 10, 6, 7, 8, 17, 7, 7, 10, 4, 8, 15, 8, 9, 9, 10, 10, 8, 10, 7, 8, 1603343, 10, 10, 10, 5, 10, 8, 9, 8, 9, 11, 10, 5, 12, 10, 9, 7, 10, 6, 9, 6, 10, 5, 5, 9, 11, 7, 9, 4742754, 9, 1117071, 13, 6, 6, 7, 7, 15, 15, 9, 7, 8, 7, 10, 8, 7, 5, 15, 11, 9, 6, 10, 7, 8, 4, 7, 11, 9, 7, 13, 5, 10, 9, 11, 8, 7, 10, 14, 9, 9, 10, 6, 10, 10, 7, 12, 7, 7, 8, 7, 12, 5, 9, 11, 7, 12, 9, 10, 6, 8, 12, 8, 9, 12, 8, 10, 9, 6428, 6, 7, 5, 11, 8, 7, 8, 8, 7, 6, 23962436, 10, 10, 11, 10, 6, 10, 15, 11, 9, 2641852, 7, 14, 5, 9, 7, 6, 7, 9, 7, 3, 15, 10, 9, 9, 9, 10, 8, 8, 10, 13, 11, 9, 10, 7, 8, 9, 13, 7, 6, 11, 12, 10, 9, 4, 10, 10, 8, 7, 10, 10, 7, 12, 15, 8, 6, 9, 12, 11, 10, 8, 8, 10, 6, 10, 8, 10, 9, 10, 13, 7, 15, 11, 8, 10, 6, 8, 8, 10, 9, 11, 8, 9, 9, 11, 8, 11, 5, 5, 5, 11, 8, 9, 3908759, 9, 8, 7, 15, 8, 9, 9, 11, 6, 6, 8, 7, 6, 4, 8, 9, 7, 9, 15, 8, 6, 17, 10, 10, 12, 9, 10, 12, 9, 6, 4, 10, 13, 8, 10, 7, 11, 13, 13, 8, 5, 12, 10, 9, 7, 11, 9, 10, 8, 3, 9, 10, 11, 10, 11, 7, 9, 8, 10, 13, 8, 8, 10, 11, 8, 13, 6, 10, 8, 9, 17209884, 11, 12, 8, 9, 9, 9, 7, 8, 8, 8, 13, 11, 7, 12, 8, 12239, 14, 9, 8, 11, 10, 7, 9, 4, 6, 10, 11, 9, 7, 14, 8, 13, 6, 9, 9, 10, 11, 8, 5439, 7, 8, 10, 12, 15, 15, 8, 9, 8, 10, 9, 9, 10, 12, 8, 9, 10, 15, 10, 6, 15, 10, 11, 5, 10, 11, 8, 6, 5, 7, 8, 7, 9, 8, 15, 6, 10, 4, 14, 9, 14, 9, 13, 12, 17, 8, 8, 10, 10, 9, 9, 10, 6, 527015334, 9, 6, 10, 12, 5, 8, 7, 5, 8, 9, 11, 10, 8, 4, 9, 8, 10, 8, 9, 7, 9, 11, 8, 9, 6, 11, 10, 10, 8, 9, 13, 9, 7, 10, 10, 6, 9, 9, 12, 8, 6, 9, 10, 9, 6, 9, 8, 9, 10, 9, 4, 7, 8, 10, 6, 15, 8, 5, 9, 6, 8, 11, 9, 9, 8, 10, 9, 8, 9, 10, 7, 9, 8, 5, 10, 8, 8, 7, 7, 8, 11, 13, 6, 10, 9, 6, 4, 8, 9, 12, 11, 8, 10, 10, 11, 15, 7, 11, 8, 13, 10, 10, 6, 5, 6, 6, 12, 9, 8, 9, 12, 5, 5, 13, 5, 8, 13, 11, 14, 8, 11, 9, 9, 9, 10, 6, 8, 5, 8, 7, 11, 11, 8, 10, 9, 10, 8, 8, 479833, 9, 8, 8, 10, 12, 10, 11, 8, 14, 15, 3, 10, 6, 10, 12, 7, 9, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2 }
{14, 11, 8, 12, 16, 11, 13, 10, 13, 8, 12, 10, 13, 13, 16, 12, 6, 13, 6, 7, 11, 12, 6, 11, 15, 6, 11, 16, 11, 11, 15, 20, 17, 14, 12, 16, 12, 17, 7, 18, 12, 3, 9, 13, 10, 6, 10, 12, 15, 7, 7, 8, 10, 22, 14, 11, 13, 12, 14, 8, 15, 16, 11, 13, 6, 6, 15, 16, 14, 9, 14, 14, 2, 14, 7, 16, 12, 12, 13, 8, 6, 11, 9, 10, 12, 7, 11, 14, 8, 10, 11, 16, 12, 9, 10, 6, 11, 14, 6, 12, 7, 13, 9, 14, 9, 9, 13, 12, 7, 22, 13, 8, 16, 14, 11, 13, 16, 5, 14, 8, 10, 4, 10, 7, 16, 8, 9, 14, 13, 15, 13, 7, 11, 14, 8, 12, 9, 13, 8, 10, 11, 8, 6, 10, 14, 12, 3, 13, 7, 8, 11, 15, 9, 8, 12, 12, 13, 14, 10, 9, 12, 15, 13, 12, 16, 13, 8, 12, 13, 11, 7, 7, 6, 12, 8, 11, 8, 13, 14, 12, 15, 4, 7, 14, 13, 13, 13, 17, 11, 13, 11, 12, 13, 6, 7, 11, 16, 77917001, 15, 12, 6, 13, 17, 8, 16, 8, 10, 14, 10, 7, 7, 14, 6, 12, 10, 17, 10, 5, 16, 7, 15, 7, 9, 11, 3, 13, 6, 15, 14, 13, 11, 12, 11, 11, 7, 12, 12, 12, 15, 22, 11, 13, 8, 12, 16, 12, 15, 11, 14, 2, 11, 9, 11, 3, 18, 4, 9, 6, 9, 8, 3, 13, 9, 12, 13, 11, 13, 14, 12, 13, 6, 14, 12, 20, 14, 11, 14, 13, 15, 10, 11, 17, 10, 7, 13, 5, 8, 12, 16, 11, 12, 14, 7, 15, 9, 15, 10, 12, 11, 13, 15, 11, 8, 14, 21, 3, 12, 8, 8, 10, 6, 8, 13, 13, 10, 6057, 10, 8, 13, 13, 18, 12, 12, 15, 14, 6, 12, 11, 9, 4, 11, 3, 15, 9, 11, 9, 10, 8, 5, 12, 5, 6, 6, 5, 11, 6, 7, 6, 18, 12, 10, 14, 13, 9, 12, 6, 6, 6, 7, 12, 8, 16, 8, 7, 12, 11, 6, 11, 9, 8, 6, 22, 7, 11, 6, 9, 15, 11, 16, 11, 12, 13, 6, 14, 11, 13, 14, 9, 9, 12, 11, 14, 6, 14, 11, 14, 15, 6, 15, 14, 7, 11, 7, 12, 12, 12, 13, 14, 11, 11, 5, 11, 13, 12, 12, 12, 13, 14, 12, 6, 10, 8, 14, 10, 3, 14, 14, 5, 18, 13, 14, 13, 8, 14, 13, 13, 8, 14, 4, 6, 9, 12, 7, 14, 13, 9, 14, 8, 14, 8, 14, 9, 14, 9, 7, 12, 8, 13, 14, 12, 15, 7, 13, 10, 17, 15, 11, 10, 14, 4, 14, 21, 13, 13, 5, 13, 5, 6, 15, 16, 11, 13, 6, 9, 8, 8, 5, 6, 8, 7, 12, 13, 13, 13, 6, 11, 13, 15, 18, 13, 12, 10, 16, 12, 13, 14, 14, 11, 14, 19, 10, 13, 6, 7, 14, 6, 8, 16, 11, 13, 9, 10, 13, 14, 13, 14, 13, 2412107, 9, 16, 13, 19, 14, 14, 15, 10, 9, 12, 14, 8, 13, 21, 12, 12, 16, 10, 13, 16, 7, 13, 13, 7, 14, 8, 7, 8, 5, 13, 10, 7, 7, 12, 6, 14, 8, 12, 12, 10, 7, 12, 27594608, 13, 10, 22, 9, 14, 11, 11, 13, 8, 10, 12, 18, 14, 13, 9, 12, 14, 16, 12, 14, 6, 13, 15, 12, 16, 12, 11, 13, 8, 14, 7, 12, 14, 14, 10, 10, 15, 12, 21, 6, 12, 8, 8, 12, 14, 19, 7, 9, 48825182, 6, 14, 7, 6, 9, 10, 6, 11, 9, 7, 7, 6, 14, 14, 16, 12, 14, 5, 15, 13, 15, 22, 9, 7, 15, 2, 15, 5, 13, 6, 12, 14, 13, 13, 14, 10, 15, 13, 13, 13, 9, 13, 10, 28320790, 11, 7, 7, 15, 13, 16, 11, 16, 6, 8, 9, 5, 9, 3, 5, 14, 21, 11, 11, 12, 11, 12, 8, 14, 12, 6, 12, 14, 9, 9, 15, 11, 7, 5, 6, 15, 14, 14, 13, 130696, 11, 22, 14, 13, 12, 11, 13, 8, 9, 12, 14, 12, 14, 8, 12, 10, 15, 12, 13, 10, 12, 13, 10, 12, 14, 4, 6, 14, 13, 9, 13, 14, 13, 7, 13, 18, 15, 13, 11, 7, 14, 12, 16, 11, 11, 12, 11, 16, 15, 12, 12, 10, 11, 12, 8, 12, 11, 6, 9, 12, 14, 9, 12, 12, 16, 8, 9, 7, 11, 13, 16, 9, 13, 10, 13, 11, 8, 7, 10, 10, 13, 11, 7, 6, 15, 12, 14, 7, 7, 9, 13, 15, 1313624, 10, 5, 15, 10, 15, 8, 6, 10, 11, 7, 13, 13, 8, 6, 13, 16, 6, 11, 10, 14, 17, 9, 9, 12, 20, 12, 13, 13, 9, 16, 15, 12, 13, 9, 11, 7, 11, 9, 14, 11, 12, 9, 11, 14, 22, 8, 13, 11, 17, 11, 10, 18, 11, 17, 18, 9, 14, 15, 8, 16, 12, 11, 11, 8, 6, 10, 14, 11, 11, 12, 12, 12, 21, 12, 15, 5, 22, 11, 11, 32288, 6, 8, 14, 14, 16, 11, 6, 10, 7, 10, 11, 8, 14, 12, 9, 13, 9, 15, 15, 6, 11, 8, 11, 13, 5, 10, 8, 12, 10, 13, 11, 9, 14, 19, 5, 13, 10, 12, 11, 12, 9, 10, 13, 14, 8, 6, 7, 14, 13, 12, 13, 14, 13, 12, 6, 13, 13, 13, 9, 5, 8, 8, 11, 9, 6, 5, 11, 10, 14, 16, 6, 4, 16, 11, 7, 8, 9, 12, 10, 11, 7098, 14, 14, 12, 17, 6, 14, 8, 12, 13, 5, 15, 14, 12, 11, 11, 8, 8, 10, 11, 14, 8}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 4, 2, 10, 8, 10, 12, 10, 6, 7, 10, 15, 9, 7, 7, 11, 9, 12, 10, 11, 7, 9, 7, 9, 4, 9, 11, 10, 6, 7, 8, 13, 9, 9, 11, 6, 12, 10, 11, 12, 11, 9, 11, 8, 12, 10, 8, 7, 10, 6, 7, 12, 9, 8, 13, 13, 7, 10, 11, 10, 6, 9, 8, 12, 10, 10, 6, 5, 10, 8, 9, 13, 10, 7, 4, 3, 7, 11, 10, 8, 7, 13, 8, 7, 8, 11, 9, 7, 10, 9, 12, 6, 11, 12, 13, 12, 11, 1893808, 6, 7, 12, 7, 13, 13, 10, 5, 9, 9, 10, 6, 7, 4, 10, 9, 11, 8, 7, 8, 10, 9, 5, 8, 161766, 6, 5, 11, 7, 14, 7, 9, 9, 10, 12, 5, 13, 10, 10, 6, 10, 12, 13, 12, 10, 7, 7, 9, 10, 8, 9, 10, 7, 9, 4, 8, 12, 8, 11, 8, 8, 9, 6, 11, 8, 7, 13, 8, 11, 2319173, 12, 6, 4, 6, 7, 13, 9, 9, 8, 9, 5, 9, 10, 7, 7, 11, 13, 11, 10, 7, 10, 12, 7, 7, 9, 10, 6, 9, 5, 3, 6, 8, 9, 9, 9, 14, 8, 11, 5, 8, 14, 7, 7, 10, 11, 8, 8, 11, 9, 13, 12, 9, 9, 12, 9, 6, 11, 8, 13, 11, 12, 15, 8, 7, 10, 12, 11, 6, 9, 9, 8, 12, 9, 10, 14, 7, 9, 12, 11, 12, 7, 9, 9, 6, 12, 12, 9, 9, 10, 10, 7, 9, 6, 10, 10, 12, 12, 13, 12, 8, 10, 11, 13, 9, 9, 8, 11, 8, 7, 7, 11, 3, 14, 14, 9, 9, 9, 8, 10, 8, 11, 13, 6, 11, 14, 12, 7, 4, 7, 13, 7, 9, 8, 9, 10, 8, 8, 8, 9, 5, 11, 10, 8, 9, 8, 9, 12, 9, 8, 12, 6, 12, 10, 8, 837410, 14, 12, 13, 6, 9, 11, 11, 8, 9, 9, 8, 10, 6, 7, 11, 6, 10, 11, 9, 11, 13, 9, 11, 10, 12, 8, 7, 5, 9, 11, 12, 9, 10, 8, 10, 4, 11, 6, 12, 15, 15, 9, 6, 8, 11, 7, 5, 11, 13, 10, 9, 10, 9, 11, 6, 7, 7, 10, 5, 9, 9, 10, 6, 9, 9, 15, 5, 7, 8, 12, 9, 11, 13, 9, 6, 11, 7, 8, 9, 8, 9, 11, 4, 10, 13, 8, 10, 12, 5, 9, 7, 12, 11, 5, 6, 5, 9, 11, 7, 13, 11, 10, 6, 9, 9, 8, 7, 10, 14, 7, 10, 7, 7, 12, 6, 11, 10, 13, 9, 10, 10, 11, 10, 13, 8, 6, 10, 7, 10, 10, 9, 10, 5, 7, 10, 9, 12, 8, 12, 6, 14, 10, 8, 14, 9, 6, 6, 6, 5, 10, 10, 13, 12, 6, 13, 11, 9, 13, 8, 5, 6, 11, 11, 9, 7, 3, 7, 9, 5, 10, 10, 8, 8, 8, 12, 7, 6, 10, 14, 12, 10, 10, 9, 9, 6, 12, 7, 12, 10, 11, 4, 11, 5, 11, 7, 14, 13, 10, 6, 6, 7, 8, 7, 5, 12, 8, 7, 6, 8, 13, 7, 5, 10, 14, 10, 10, 13, 7, 9, 7, 5, 13, 14, 14, 7, 8, 6, 12, 9, 12, 4, 11, 14, 12, 14, 12, 13, 4, 8, 8, 13, 6, 10, 13, 11, 8, 10, 9, 8, 9, 7, 9, 6, 11, 5, 7, 11, 10, 6, 6, 9, 6, 9, 9, 10, 8, 10, 6, 12, 9, 13, 15, 5, 10, 10, 6, 8, 9, 10, 8, 8, 6, 10, 4, 13, 9, 9, 10, 7, 6, 10, 9, 6, 10, 8, 9, 7, 8, 13, 9, 7, 11, 12, 11, 10, 11, 8, 12, 10, 8, 11, 7, 11, 13, 8, 6, 7, 12, 5, 6, 6, 6, 11, 6, 11, 9, 7, 7, 11, 7, 15, 13, 9, 7, 8, 12, 7, 12, 9, 13, 8, 9, 8, 11, 13, 12, 7, 6, 9, 11, 8, 7, 14, 12, 8, 10, 12, 7, 9, 12, 7, 11, 10, 11, 7, 5, 8, 9, 6, 11, 9, 5, 5, 12, 5, 9, 10, 11, 9, 5, 7, 11, 8, 11, 14, 9, 6, 9, 10, 7, 11, 6, 11, 12, 10, 6, 8, 6, 7, 11, 8, 9, 7, 8, 12, 9, 8, 12, 12, 6, 14, 7, 6, 10, 7, 5, 9, 3, 9, 12, 7, 8, 11, 4, 5, 5, 9, 8, 10, 8, 9, 13, 8, 10, 10, 8, 10, 11, 7, 9, 9, 11, 9, 9, 4, 8, 8, 13, 6, 9, 9, 8, 9, 7, 13, 11, 7, 10, 8, 5, 7, 12, 11, 10, 3, 9, 4, 9, 11, 6, 8, 10, 7, 7, 7, 12, 8, 11, 12, 9, 9, 12, 13, 8, 7, 6, 8, 6, 6, 11, 9, 7, 9, 8, 6, 5, 9, 10, 13, 9, 13, 12, 11, 6, 5, 11, 6, 7, 9, 5, 10, 9, 12, 6, 12, 10, 9, 7, 8, 10, 4, 7, 6, 10, 6, 7, 10, 8, 11, 8, 8, 9, 10, 10, 5, 6, 8, 9, 3, 10, 9, 6, 13, 7, 6, 13, 10, 11, 10, 11, 13, 9, 9, 10, 8, 13, 9, 14, 10, 9, 12, 14, 6, 8, 8, 8, 7, 13, 11, 6, 5, 11, 7, 8, 12, 11, 9, 9, 15, 8, 5, 12, 9, 9, 9, 12, 11, 10, 4, 12, 9, 4, 5, 9, 5, 12, 10, 10, 7, 12, 12, 10, 14, 6, 12, 12, 6, 13, 10, 8, 10, 8, 8, 8, 12, 5, 7, 14, 5, 6, 5, 9, 11, 13, 10, 8, 9, 14, 13, 13, 10, 14, 11, 6, 10, 11, 7, 10, 15, 12, 11, 9}

Returns: {-1 }
{12, 9, 5, 9, 8, 6, 12, 6, 10, 9, 6, 15, 9, 10, 8, 8, 12, 8, 9, 11, 7, 10, 9, 12, 12, 6, 6, 5, 4, 12, 5, 11, 16, 16, 7, 14, 11, 13, 11, 8, 13, 9, 7, 5, 10, 15, 9, 10, 9, 14, 6, 7, 8, 10, 6, 14, 9, 10, 9, 9, 13, 16, 9, 9, 8, 12, 8, 6, 10, 16, 12, 9, 5, 11, 11, 12, 10, 8, 6, 10, 9, 9, 13, 8, 5, 7, 10, 13, 8, 15, 10, 7, 16, 8, 15, 10, 14, 5, 9, 5, 5, 10, 12, 7, 5, 13, 7, 11, 7, 12, 16, 8, 9, 13, 17, 5, 16, 8, 12, 7, 15, 8, 12, 10, 13, 9, 12, 7, 7, 5, 9, 11, 7, 8, 9, 6, 8, 9, 9, 7, 7, 11, 9, 8, 5, 11, 14, 10, 13, 7, 8, 11, 8, 11, 5, 10, 11, 6, 6, 7, 8, 11, 10, 13, 11, 10, 7, 6, 9, 7, 9, 14, 4, 12, 5, 14, 9, 10, 12, 4, 5, 12, 11, 7, 3, 11, 10, 11, 8, 4, 9, 9, 8, 7, 5, 14, 10, 11, 10, 8, 10, 14, 6, 15, 10, 7, 11, 6, 15, 8, 4, 9, 11, 13, 9, 11, 9, 4, 10, 8, 11, 8, 9, 14, 12, 7, 319341087, 9, 17, 4, 8, 10, 4, 7, 14, 7, 11, 9, 6, 9, 8, 8, 10, 9, 7, 7, 5, 8, 6, 6, 5, 10, 9, 4, 7, 11, 11, 9, 6, 10, 9, 15, 5, 6, 6, 11, 5, 11, 10, 8, 4, 10, 10, 8, 9, 8, 6, 8, 6, 10, 21233, 11, 18, 14, 16, 11, 12, 10, 12, 7, 9, 9, 11, 10, 10, 8, 10, 13, 10, 13, 11, 11, 8, 8, 10, 13, 5, 11, 8, 11, 14, 13, 5, 14, 5, 15, 8, 9, 9, 9, 5, 13, 11, 5, 12, 9, 10, 10, 16, 12, 5, 13, 15, 8, 8, 13, 10, 12, 10, 11, 8, 9, 8, 8, 9, 14, 7, 5, 6, 5, 8, 11, 10, 7, 14, 12, 7, 7, 8, 11, 9, 9, 10, 10, 12, 5, 9, 10, 6, 7, 6, 5, 14, 8, 14, 9, 9, 11, 16, 8, 10, 12, 6, 7, 10, 12, 10, 6, 11, 6079, 6, 8, 14, 10, 7, 9, 13, 5, 5, 10, 13, 4, 9, 18, 12, 6, 8, 16, 9, 7, 4, 8, 11, 11, 12, 12, 6, 8, 9, 15, 8, 8, 10, 8, 5, 10, 8, 6, 7, 5, 8, 12, 9, 8, 11, 13, 13, 7, 12, 7, 13, 6, 9, 6, 10, 10, 7, 11, 10, 12, 5, 11, 11, 13, 10, 5, 6, 10, 8, 12, 13, 14, 15, 10, 9, 8, 4, 11, 10, 9, 12, 13, 7, 15, 11, 10, 10, 11, 9, 6, 13, 11, 6, 7, 8, 8, 11, 11, 4, 12, 9, 9, 9, 9, 6, 14, 11, 13, 9, 13, 5, 7, 11, 13, 5, 7, 10, 10, 11, 5, 10, 11, 12, 7, 6, 6, 10, 7, 14, 10, 6, 11, 14, 9, 13, 9, 11, 9, 12, 10, 5, 9, 12, 14, 6, 9, 11, 14, 6, 9, 10, 14, 11, 10, 8, 10, 13, 4, 10, 5, 5, 4, 8, 7, 6, 11, 5, 9, 11, 5, 4, 5, 11, 9, 9, 11, 12, 9, 4, 14, 11, 9, 7, 5, 11, 17, 16, 9, 8, 6, 6, 8, 9, 9, 10, 4, 8, 10, 15, 4, 10, 9, 6, 7, 7, 8, 7, 4, 7, 9, 14, 10, 10, 9, 7, 9, 9, 4, 12, 6, 9, 7, 5, 10, 10, 10, 7, 9, 8, 6, 5, 9, 13, 11, 5, 13, 15, 10, 10, 15, 10, 5, 13, 4, 15, 16, 10, 15, 14, 13, 9, 5, 7, 12, 10, 3, 10, 14, 12, 7, 12, 12, 6, 12, 13, 9, 10, 8, 7, 1508513, 11, 8, 5, 10, 6, 12, 8, 9, 7, 15, 11, 5, 12, 12, 10, 6, 8, 10, 6, 5, 3, 10, 12, 9, 12, 12, 7, 6, 11, 18, 5, 6, 11, 10, 10, 11, 11, 10, 9, 8, 15, 6, 11, 12, 16, 13, 11, 9, 13, 9, 11, 13, 12, 8, 6, 14, 11, 6, 10, 12, 12, 4, 6, 14, 10, 3, 12, 8, 10, 7, 15, 11, 6, 10, 10, 11, 12, 10, 6, 10, 6, 11, 13, 9, 7, 7, 11, 10, 12, 7, 10, 10, 10, 12, 14, 9, 6, 6, 8, 17, 12, 9, 6, 9, 10, 13, 9, 12, 13, 9, 8, 15, 6, 9, 27379, 5, 7, 10, 9, 9, 7, 11, 6, 8, 6, 260455685, 8, 5, 18, 9, 7, 12, 6, 9, 9, 10, 13, 13, 9, 8, 10, 11, 15, 9, 10, 14, 10, 9, 13, 18, 14, 11, 9, 6, 9, 13, 13, 4, 4, 4, 6, 12, 11, 10, 7, 11, 12, 13, 15, 13, 15, 9, 7, 10, 11, 5, 4, 9, 7, 15, 10, 13, 16, 10, 12, 7, 7, 6, 15, 11, 10, 8, 10, 5, 9, 10, 3, 4, 17, 11, 12, 12, 10, 11, 9, 12, 6, 13, 11, 13, 6, 13, 8, 6, 14, 8, 11, 9, 13, 5, 8, 10, 10, 11, 10, 17, 11, 7, 16, 11, 6, 6, 11, 6, 9, 12, 9, 16, 8, 9, 10, 14, 8, 14, 10, 10, 11, 13, 8, 11, 10, 9, 8, 8, 8, 10, 15, 14, 10, 9, 8, 5, 12, 5, 11, 8, 17, 12, 10, 14, 9, 6, 8, 239356, 13, 9, 15, 18, 7, 13, 7, 11, 10, 6, 5, 9, 5, 5, 16, 7, 7, 9, 10, 7, 14, 10, 7, 13, 13, 11, 7, 14, 12, 6, 4, 7, 10, 8}

Returns: {2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2 }
{11, 12, 8, 11, 10, 11, 7, 10, 10, 14, 7, 10, 13, 11, 14, 12, 13, 9, 13, 11, 11, 7, 9, 11, 13, 12, 14, 9, 7, 6, 7, 11, 8, 5, 11, 9, 7, 12, 13, 12, 10, 9, 16, 8, 12, 6, 12, 15, 6, 10, 11, 6, 8, 11, 12, 7, 12, 7, 12, 13, 10, 13, 13, 13, 10, 12, 11, 11, 11, 7, 11, 8, 7, 6, 13, 13, 6, 13, 12, 10, 14, 14, 11, 12, 12, 11, 9, 6, 13, 14, 9, 8, 10, 13, 10, 15, 7, 5, 12, 15, 11, 11, 12, 8, 8, 8, 8, 7, 11, 12, 13, 10, 12, 11, 8, 13, 9, 9, 13, 7, 7, 11, 5, 11, 7, 7, 14, 5, 10, 8, 9, 15, 9, 11, 10, 14, 11, 12, 14, 10, 8, 9, 8, 6, 12, 11, 6, 7, 14, 13, 9, 12, 13, 12, 6, 12, 13, 8, 12, 13, 14, 10, 9, 11, 10, 5, 8, 14, 10, 9, 8, 11, 9, 14, 12, 11, 9, 12, 11, 11, 11, 12, 6, 10, 12, 10, 14, 8, 14, 11, 13, 4, 5, 4, 8, 10, 6, 12, 10, 11, 13, 9, 10, 7, 12, 10, 8, 10, 8, 11, 12, 6, 8, 3, 11, 7, 3, 9, 6, 14, 12, 11, 10, 7, 13, 13, 13, 9, 10, 8, 11, 9, 13, 8, 10, 7, 8, 13, 7, 12, 11, 13, 7, 10, 10, 5, 8, 7, 13, 4, 12, 14, 7, 6, 10, 6, 12, 12, 11, 11, 14, 13, 8, 14, 7, 11, 3, 12, 12, 9, 9, 11, 11, 6, 11, 7, 15, 11, 13, 13, 9, 11, 7, 5, 13, 9, 9, 9, 10, 11, 11, 8, 11, 11, 12, 12, 12, 10, 11, 10, 9, 11, 8, 15, 8, 9, 13, 5, 7, 12, 11, 8, 11, 8, 10, 9, 9, 4, 9, 13, 13, 15, 5, 7, 9, 7, 10, 9, 11, 13, 12, 11, 11, 12, 6, 8, 9, 8, 6, 13, 15, 10, 9, 10, 11, 11, 12, 13, 10, 9, 11, 9, 13, 11, 10, 8, 7, 12, 6, 10, 13, 9, 10, 6, 11, 10, 11, 9, 12, 10, 13, 8, 11, 12, 9, 11, 14, 11, 9, 10, 14, 12, 12, 13, 13, 11, 7, 13, 5, 10, 9, 13, 7, 10, 5, 14, 11, 13, 12, 13, 6, 4, 13, 15, 11, 13, 10, 12, 8, 9, 9, 11, 15, 6, 12, 10, 10, 12, 15, 9, 11, 12, 9, 8, 7, 8, 5, 14, 2, 14, 13, 10, 11, 7, 13, 12, 12, 9, 9, 8, 11, 14, 15, 11, 11, 8, 14, 7, 9, 10, 12, 8, 5, 13, 8, 11, 13, 12, 8, 8, 13, 13, 11, 14, 11, 8, 12, 10, 13, 4, 5, 9, 7, 12, 12, 14, 11, 12, 11, 9, 14, 7, 12, 11, 13, 14, 8, 11, 13, 8, 9, 12, 7, 10, 14, 8, 9, 8, 11, 15, 9, 12, 13, 11, 11, 9, 13, 13, 8, 9, 12, 11, 14, 13, 4, 14, 5, 13, 11, 7, 11, 10, 10, 11, 9, 9, 11, 6, 8, 14, 2, 12, 11, 6, 11, 10, 10, 10, 12, 7, 11, 9, 11, 14, 12, 6, 8, 11, 7, 11, 11, 5, 12, 11, 9, 12, 10, 8, 12, 15, 11, 9, 12, 11, 7, 9, 10, 12, 12, 14, 7, 12, 13, 13, 13, 14, 11, 6, 10, 11, 9, 10, 9, 12, 8, 13, 11, 8, 10, 8, 10, 9, 8, 15, 11, 11, 9, 8, 11, 11, 12, 11, 12, 9, 14, 11, 11, 7, 8, 8, 7, 8, 11, 11, 12, 13, 5, 8, 16, 10, 12, 11, 15, 12, 8, 12, 4, 15, 11, 8, 8, 11, 12, 14, 12, 9, 10, 11, 10, 11, 5, 14, 14, 10, 13, 9, 6, 13, 11, 12, 12, 9, 10, 12, 13, 6, 12, 12, 11, 14, 11, 5, 4, 13, 13, 5, 7, 14, 11, 14, 7, 12, 10, 9, 9, 8, 9, 7, 13, 12, 11, 10, 7, 14, 10, 7, 13, 12, 13, 10, 12, 7, 12, 11, 10, 9, 9, 7, 2, 6, 9, 7, 12, 6, 15, 7, 13, 14, 9, 12, 8, 10, 7, 8, 12, 9, 14, 9, 10, 6, 7, 13, 15, 8, 11, 14, 12, 11, 11, 11, 8, 10, 11, 14, 8, 7, 9, 11, 8, 14, 15, 15, 12, 11, 9, 8, 13, 8, 6, 10, 6, 8, 12, 7, 11, 15, 5, 7, 13, 12, 8, 12, 9, 11, 12, 12, 13, 15, 10, 9, 9, 9, 9, 6, 9, 9, 11, 10, 12, 7, 11, 10, 11, 14, 10, 8, 14, 12, 5, 7, 13, 11, 13, 11, 9, 8, 8, 7, 8, 8, 8, 11, 13, 11, 11, 7, 13, 4, 7, 2, 11, 9, 13, 10, 13, 7, 13, 11, 4, 3, 13, 10, 13, 8, 6, 10, 8, 14, 8, 12, 11, 7, 15, 8, 4, 11, 13, 10, 11, 5, 10, 6, 12, 8, 9, 11, 13, 11, 9, 12, 10, 15, 10, 6, 15, 4, 9, 11, 7, 11, 11, 7, 8, 9, 5, 6, 11, 16, 10, 7, 10, 7, 11, 12, 11, 10, 6, 13, 12, 15, 6, 9, 9, 12, 14, 8, 13, 6, 10, 4, 10, 7, 11, 12, 9, 11, 12, 11, 11, 14, 7, 5, 12, 8, 6, 6, 14, 13, 13, 15, 14, 8, 5, 11, 13, 11, 10, 11, 9, 9, 12, 11, 12, 7, 14, 7, 11, 14, 12, 9, 7, 15, 8, 13, 8, 9, 8, 8, 11, 10, 11, 11, 12, 11, 8, 13, 11, 13, 9, 10, 7, 10, 11, 13, 9, 7, 13, 7, 8, 9, 12, 13, 9, 8, 11, 11, 11, 8, 11, 11, 13, 11, 14, 10, 11, 10, 14, 12, 7, 12, 12, 6, 9, 11, 11, 12, 8, 12, 8, 12, 7, 13, 9, 12, 13, 8, 12, 14, 11}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 10, 13, 7, 10, 10, 14, 12, 5, 12, 5, 8, 18, 9, 9, 9, 10, 12, 11, 6, 12, 11, 9, 16, 11, 8, 12, 16, 7, 7, 11, 7, 11, 5, 7, 11, 19, 5, 15, 11, 14, 8, 15, 3, 7, 10, 15, 8, 14, 7, 10, 6, 3, 11, 4, 11, 8, 14, 10, 10, 11, 17, 6, 15, 11, 10, 11, 16, 9, 14659, 11, 11, 7, 5, 6, 15, 10, 15, 15, 9, 11, 10, 6, 6, 14, 9, 9, 6, 15, 12, 11, 6, 13, 6, 10, 8, 6, 13, 11, 11, 13, 11, 10, 9, 16, 14, 6, 11, 11, 7, 11, 13, 9, 15, 3, 7, 7, 5, 5, 12, 14, 9, 12, 5, 8, 8, 8, 10, 11, 5, 11, 13, 7, 15, 9, 9, 11, 12, 12, 15, 14, 13, 8, 5, 9, 12, 12, 9, 7, 11, 12, 5, 6, 10, 3, 8, 10, 10, 10, 10, 13, 16, 9, 14, 11, 9, 12, 15, 13, 7, 12, 4, 12, 10, 11, 11, 12, 11, 13, 16, 11, 6, 8, 6, 4, 4, 12, 11, 11, 13, 12, 6, 7, 10, 6, 9, 11, 6, 9, 14, 16, 6, 13, 5, 7, 7, 12, 8, 11, 12, 10, 15, 12, 5, 14, 14, 15377331, 11, 9, 14, 11, 7, 12, 11, 9, 14, 8, 10, 10, 7, 6, 13, 10, 11, 15, 5, 12, 6, 14, 10, 21, 6, 9, 12, 6, 13, 10, 12, 7, 9, 14, 11, 8, 4, 9, 14, 11, 13, 6, 6, 13, 11, 9, 8, 8, 11, 10, 6, 12, 7, 4, 10, 13, 18, 14, 13, 10, 14, 12, 4, 13, 11, 6, 7, 15, 8, 11, 8, 4, 13, 7, 14, 7, 7, 7, 8, 9, 6, 10, 12, 5, 7, 8, 13, 10, 7, 11, 14, 10, 5, 16, 5, 13, 9, 10, 8, 13, 6, 7, 16, 13, 9, 14, 13, 11, 8, 6, 7, 13, 15, 10, 12, 13, 11, 6, 7, 17, 14, 8, 208919391, 11, 15, 15, 10, 6, 14, 11, 12, 12, 10, 7, 14, 9, 6, 10, 15, 11, 10, 8, 11, 6, 12, 15, 11, 7, 9, 5, 7, 10, 11, 10, 10, 11, 17, 7, 8, 12, 13, 12, 10, 9, 11, 11, 13, 9, 12, 13, 8, 7, 11, 8, 11, 14, 8, 12, 16, 11, 9, 12, 6, 13, 9, 11, 13, 12, 12, 6, 10, 17, 10, 7, 8, 7, 6, 11, 13, 15, 11, 7, 9, 9, 14, 7, 8, 5, 11, 8, 12, 10, 3, 12, 9, 11, 7, 4, 9, 6, 10, 10, 13, 7, 21, 11, 13, 10, 8, 14, 10, 13, 11, 11, 11, 12, 10, 12, 13, 1229, 12, 9, 10, 12, 15, 7, 12, 11, 14, 12, 252396, 17, 10, 4, 10, 14, 6, 6, 7, 6, 8, 8, 12, 6, 8, 9, 13, 16, 6, 12, 14, 13, 9, 8, 14, 7, 15, 15, 10, 5, 12, 14, 14, 5, 14, 11, 8, 7, 59127603, 12, 15, 12, 14, 50718994, 11, 7, 16, 11, 2921, 13, 13, 11, 15, 10, 11, 10, 11, 9, 13, 3, 6, 21, 10, 5, 14, 13, 19, 6, 8, 9, 10, 6, 12, 3, 12, 11, 11, 8, 10, 336741638, 9, 13, 14, 9, 8, 7, 13, 10, 8, 11, 14, 14, 7, 14, 10, 14, 11, 12, 8, 7, 13, 15, 11, 12, 10, 7, 12, 11, 9, 6, 5, 14, 8, 6, 15, 12, 16, 6, 13, 10, 8, 9, 7, 11, 12, 12, 7, 9, 14, 8, 13, 14, 10, 4, 13, 12, 8, 10, 7, 16, 12, 13, 14, 10, 15, 13, 8, 15, 13, 12, 13, 17, 13, 11, 13, 13, 12, 7, 10, 8, 10, 9, 7, 12, 10, 15, 5, 8, 3, 7, 11, 9, 11, 6, 4, 9, 4, 6, 9, 11, 14, 11, 7, 8, 12, 10, 9, 4, 13, 9, 6, 13, 10, 102201, 6, 10, 9, 17, 13, 10, 9, 6, 8, 9, 8, 12, 11, 12, 7, 12, 6, 8, 12, 14, 6, 9, 11, 14, 4, 8, 7, 6, 9, 11, 18, 8, 16, 3362, 7, 10, 12, 14, 11, 5, 8, 11, 12, 9, 6, 5, 9, 9, 12, 3, 14, 10, 9, 8, 14, 7, 10, 9, 10, 4, 13, 15, 13, 9, 15, 14, 9, 7, 14, 8, 10, 11, 11, 11, 11, 14, 15373796, 11, 16, 5, 13, 12, 10, 12, 9, 16, 14, 8, 8, 13, 11, 14, 8, 11, 7, 8, 13, 13, 14, 11, 11, 11, 12, 12, 8, 11, 4, 9, 16, 10, 11, 12, 7, 9, 6, 6, 7, 20, 7, 14, 13, 10, 10, 8, 8, 6, 6, 8, 7, 10, 12, 10, 5, 8, 12, 10, 8, 15, 9, 14, 16, 12, 14, 11, 18, 11, 9, 9, 6, 7, 12, 7, 5, 10, 3, 4, 3, 8, 10, 10, 6, 7, 11, 8, 8, 9, 4, 8, 14, 16, 15, 14, 15, 10, 10, 1352, 11, 12, 2816843, 13, 10, 8, 8, 10, 6, 6, 6, 8, 5, 11, 11, 9, 10, 20, 15, 8, 11, 10, 6, 10, 17, 10, 9, 8, 11, 7, 12, 9, 7, 8, 15, 7, 10, 14, 9, 10, 14, 8, 9, 11, 12, 12, 7, 7, 9, 10, 8, 7, 12, 8, 10, 14, 12, 8, 9, 6, 8, 15, 15, 11, 28537052, 7, 11, 8, 6, 11, 17, 9, 9, 17, 15, 6, 12, 5, 4, 12, 13, 7, 10, 8, 9, 9, 7, 7, 6, 13, 11, 13, 8, 10, 10, 9, 18, 13, 13, 8, 11, 4, 12, 15, 10, 6, 5, 15, 10, 7, 8, 9, 29735580, 11, 8, 14, 11, 13, 9, 5, 7, 8, 8, 11, 10, 8, 8, 9, 10, 3, 9, 9, 12, 12, 9, 7, 13, 12553, 12, 6, 9, 10, 10}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 9, 11, 6, 9, 9, 6, 9, 7, 10, 5, 7, 9, 13, 8, 6, 11, 9, 12, 12, 6, 8, 9, 6, 8, 7, 6, 10, 7, 8, 8, 7, 12, 9, 8, 10, 8, 4, 12, 8, 11, 8, 9, 7, 8, 9, 10, 8, 8, 12, 8, 12, 13, 9, 9, 10, 8, 7, 8, 9, 9, 7, 7, 11, 9, 8, 8, 12, 5, 10, 10, 6, 9, 9, 8, 6, 5, 10, 7, 7, 8, 4, 9, 10, 13, 8, 9, 9, 7, 7, 9, 6, 8, 8, 9, 12, 11, 11, 5, 8, 12, 7, 13, 9, 7, 10, 7, 9, 6, 9, 10, 8, 10, 11, 9, 11, 9, 10, 10, 8, 7, 9, 9, 12, 4, 6, 6, 9, 12, 9, 10, 2, 10, 8, 9, 10, 8, 10, 11, 7, 5, 10, 8, 10, 6, 7, 13, 12, 8, 11, 9, 12, 6, 8, 11, 10, 11, 8, 10, 6, 9, 5, 10, 7, 10, 12, 7, 8, 10, 8, 6, 6, 6, 9, 10, 7, 9, 11, 7, 9, 9, 11, 11, 10, 10, 7, 5, 7, 11, 11, 11, 9, 6, 9, 8, 8, 4, 12, 7, 10, 10, 9, 8, 11, 8, 7, 11, 6, 8, 13, 8, 7, 12, 7, 7, 9, 7, 4, 7, 10, 6, 9, 8, 5, 8, 10, 11, 8, 7, 8, 8, 9, 6, 9, 6, 9, 8, 9, 9, 11, 12, 8, 8, 9, 4, 11, 13, 9, 6, 8, 9, 11, 11, 8, 8, 9, 9, 8, 6, 12, 7, 8, 8, 9, 10, 11, 11, 6, 10, 10, 9, 9, 9, 8, 7, 9, 7, 9, 6, 6, 7, 8, 10, 5, 7, 10, 8, 9, 5, 6, 11, 11, 11, 6, 9, 9, 9, 11, 10, 6, 7, 10, 8, 7, 6, 12, 10, 10, 8, 11, 8, 11, 9, 9, 6, 4, 9, 11, 6, 6, 8, 13, 11, 10, 9, 7, 8, 5, 7, 11, 9, 10, 7, 12, 9, 10, 5, 10, 10, 8, 9, 14, 9, 9, 6, 9, 6, 10, 11, 8, 9, 7, 10, 6, 10, 5, 11, 9, 10, 8, 9, 11, 10, 6, 8, 9, 6, 7, 8, 6, 6, 9, 9, 11, 10, 9, 6, 10, 9, 13, 9, 6, 9, 11, 9, 10, 10, 11, 8, 5, 13, 7, 11, 5, 8, 7, 7, 8, 8, 9, 9, 9, 7, 7, 7, 11, 11, 9, 13, 8, 12, 7, 8, 10, 9, 9, 8, 5, 5, 6, 13, 10, 11, 10, 7, 8, 13, 9, 8, 8, 6, 11, 5, 8, 10, 8, 8, 9, 9, 7, 11, 10, 6, 7, 9, 4, 8, 9, 11, 7, 6, 9, 7, 9, 6, 10, 8, 10, 12, 5, 7, 11, 10, 8, 8, 5, 9, 7, 9, 7, 9, 12, 11, 13, 10, 13, 6, 8, 7, 8, 10, 9, 10, 9, 11, 6, 10, 13, 10, 11, 6, 5, 12, 10, 7, 12, 8, 11, 10, 6, 11, 10, 6, 12, 11, 8, 11, 7, 10, 5, 12, 9, 7, 8, 8, 7, 7, 6, 9, 9, 12, 6, 6, 12, 6, 12, 11, 12, 9, 8, 9, 7, 8, 7, 11, 12, 11, 8, 11, 6, 9, 8, 8, 8, 8, 6, 9, 9, 10, 9, 8, 8, 6, 6, 6, 5, 6, 8, 12, 11, 6, 8, 7, 13, 11, 9, 9, 8, 9, 10, 8, 4, 7, 12, 8, 6, 8, 7, 6, 12, 6, 9, 9, 5, 11, 8, 12, 8, 8, 7, 6, 9, 8, 6, 10, 11, 7, 5, 9, 6, 6, 6, 9, 8, 6, 8, 11, 9, 8, 8, 10, 11, 10, 7, 8, 11, 6, 10, 8, 5, 9, 10, 8, 5, 9, 9, 7, 12, 9, 6, 8, 8, 10, 6, 10, 10, 6, 9, 11, 7, 7, 9, 12, 9, 6, 9, 9, 8, 10, 9, 9, 9, 4, 9, 12, 4, 11, 12, 7, 8, 7, 6, 11, 10, 5, 10, 11, 8, 7, 6, 7, 11, 9, 5, 7, 9, 6, 9, 10, 10, 11, 8, 11, 9, 10, 8, 9, 9, 9, 12, 4, 10, 11, 7, 10, 9, 11, 10, 10, 8, 10, 7, 12, 7, 12, 5, 11, 13, 12, 4, 10, 9, 10, 9, 10, 10, 9, 7, 6, 9, 7, 12, 7, 10, 10, 6, 10, 6, 11, 7, 12, 9, 7, 9, 7, 9, 9, 8, 8, 12, 11, 9, 9, 8, 9, 11, 11, 12, 6, 9, 10, 11, 8, 9, 6, 7, 13, 9, 6, 5, 7, 6, 9, 12, 9, 4, 10, 11, 6, 4, 5, 7, 12, 9, 9, 5, 8, 10, 6, 10, 10, 7, 7, 8, 6, 7, 7, 6, 10, 12, 6, 7, 10, 11, 6, 8, 6, 9, 10, 11, 6, 12, 6, 7, 10, 2, 7, 9, 12, 6, 358155292, 7, 8, 10, 6, 11, 5, 8, 9, 5, 9, 8, 9, 9, 7, 7, 7, 8, 6, 12, 8, 9, 9, 10, 9, 8, 9, 8, 10, 6, 10, 10, 9, 8, 10, 9, 7, 10, 6, 11, 10, 7, 7, 8, 9, 9, 8, 8, 9, 8, 10, 8, 7, 8, 10, 11, 7, 10, 7, 10, 10, 6, 5, 10, 9, 10, 7, 12, 6, 11, 7, 11, 7, 11, 7, 6, 9, 9, 9, 8, 5, 6, 7, 6, 10, 10, 7, 7, 8, 6, 10, 6, 10, 10, 11, 11, 14, 7, 7, 10, 10, 7, 12, 8, 10, 11, 11, 9, 6, 6, 10, 7, 9, 5, 9, 8, 5, 8, 7, 6, 9, 9, 12, 9, 12, 11, 6, 13, 8, 10, 6, 9, 11, 7, 3, 8, 9, 7, 10, 10, 8, 9, 8, 8, 7, 10, 8, 12, 6, 9, 7, 10, 5, 9, 9, 10, 8, 8, 8, 6, 11, 6, 4, 10, 7, 6, 11, 9, 3, 7, 7, 10, 11, 10, 10, 5, 9, 3, 7, 9, 8, 3, 8, 6, 6, 9, 14, 9, 10, 9}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2 }
{10, 8, 9, 10, 6, 17597447, 11, 10, 12, 9, 7, 10, 8, 7, 12, 10, 8, 7, 7, 10, 11, 6, 8, 11, 12, 7, 13, 9, 12, 9, 8, 8, 6, 11, 9, 8, 6, 8, 10, 9, 10, 151879912, 9, 9, 8, 10, 12, 120082908, 8, 6, 9, 8, 12, 13, 10, 9, 8, 10, 11, 8, 4, 10, 10, 8, 8, 9, 9, 10, 12, 11, 9, 10, 6, 10, 8, 11, 8, 11, 10, 10, 12, 11, 13, 10, 9, 7, 8, 8, 6, 10, 14, 9, 7, 12, 12, 6, 8, 10, 8, 9, 8, 9, 5, 10, 9, 9, 13, 9, 12, 9, 247524569, 10, 8, 7, 12, 4, 10, 12, 10, 8, 10, 11, 6, 9, 9, 11, 8, 3770, 8, 10, 8, 6, 8, 13, 11, 2, 10, 7, 11, 14, 9, 13, 12, 10, 4, 11, 10, 7, 8, 13, 9, 7, 12, 10, 7, 8, 10, 8, 9, 13, 9, 6, 5, 11, 9, 7, 6, 74737, 9, 5, 9, 11, 9, 11, 13, 7, 11, 11, 10, 10, 7, 45772, 10, 8, 8, 10, 9, 11, 11, 9, 5, 10, 9, 12, 10, 7, 13, 14, 12, 9, 9, 9, 9, 1807362, 9, 6, 9, 1219073, 4, 8, 10, 9, 12, 11, 11, 9, 9, 8, 11, 9, 11, 13, 8, 5, 12, 10, 9, 8, 8, 8, 7, 9, 4, 9, 9, 11, 12, 8, 5, 9, 9, 6, 104541, 10, 6, 8, 10, 10, 10, 11, 9, 11, 9, 9, 12, 12, 9, 12, 10, 11, 10, 10, 12, 10, 9, 6, 11, 11, 6, 10, 9, 12, 9, 10, 9, 10, 9, 7, 8, 11, 6, 5, 7, 11, 8, 6, 9, 11, 10, 10, 11, 11, 10, 11, 11, 10, 8, 11, 10, 12, 6, 5, 9, 9, 7, 9, 2462, 5, 14, 12, 5, 8, 8, 12, 9, 11, 7, 8, 9, 11, 8, 6, 5, 10, 13, 12, 522550, 9, 7, 8, 8, 11, 10, 11, 8, 8, 9, 7, 6, 7, 8, 3, 13, 9, 11, 8, 12, 11, 8, 11, 6, 7, 12, 7, 9, 8, 8, 7, 8, 6, 8, 10, 13, 13, 12, 13, 7, 10, 7, 11, 6, 10, 11, 9, 7, 9, 11, 13, 8, 11, 7, 10, 13, 7, 10, 8, 8, 7, 10, 8, 5, 11, 6, 9, 6, 3, 6, 10, 10, 7, 8, 10, 9, 8, 9, 12, 10, 8, 11, 7, 8, 8, 7, 11, 9, 13, 9, 8, 10, 6, 5, 11, 4, 11, 13, 9, 8, 13, 9, 7, 10, 7, 9, 6, 10, 11, 9, 5, 7, 9, 14, 8, 9, 7, 8, 11, 8, 7, 2051, 8, 9, 10, 8, 4784, 9, 6, 9, 13, 7, 6, 10, 10, 12, 13, 7, 7, 12, 8, 8, 7, 11, 10, 9, 3, 8, 9, 14, 8, 6, 5, 11, 8, 7, 9, 423856, 8, 11, 8, 7, 9, 90804264, 12, 10, 248154904, 7, 6, 8, 10, 9, 11, 11, 7, 251884158, 11, 4, 11, 10, 7, 10, 6, 12, 8, 10, 12, 6, 8, 13, 9, 12, 11, 7, 13, 10, 9, 12, 10, 10, 11, 4, 9, 9, 13, 11, 9, 9, 10, 9, 10, 10, 8, 7, 10, 5, 11, 9, 8, 9, 12, 7, 10, 8, 7, 11, 11, 11, 13, 10, 9, 2224247, 23087, 13, 9, 9, 10, 10, 8, 10, 11, 5, 11, 10, 69507, 5, 9, 9, 8, 9, 12, 8, 8, 11, 8, 11, 3, 10, 12, 12, 12, 10, 8, 10, 8, 11, 7, 8, 8, 7, 8, 10, 10, 10, 12, 14, 9, 10, 11, 10, 10, 9, 9, 5, 11, 10, 6, 9, 10, 12, 8, 9, 8, 13, 11, 7, 5, 9, 9, 13, 11, 8, 7, 7, 6, 12, 9, 9, 12, 8, 8, 11, 8, 9, 9, 12, 8, 9, 10, 8, 7, 9, 13, 10, 4, 9, 9, 10, 6, 8, 11, 9, 10, 11, 8, 11, 5, 12, 10, 11, 1991753, 9, 8, 9, 11, 11, 10, 7, 9, 11, 9, 8, 7, 7, 234564, 14, 10, 11, 8, 9, 9, 9, 5, 13, 8, 8, 6, 10, 8, 10, 9, 10, 11, 9, 11, 8, 12, 8, 11, 10, 10, 10, 11, 8, 10, 11, 11, 11, 11, 8, 10, 12, 8, 8, 6, 12, 7, 9, 10, 12, 6, 12, 11, 6, 10, 9, 5, 9, 5, 12, 13, 12, 11, 6, 10, 10, 9, 9, 8, 11, 8, 8, 8, 14387, 7, 12, 9, 5, 9, 8, 8, 9, 8, 10, 13, 10, 12, 7, 9, 8, 10, 10, 8, 9, 9, 7, 11, 9, 8, 8, 5, 5, 8, 11, 11, 8, 10, 7, 14, 7, 6, 10, 5, 7, 8, 4, 12, 11, 8, 10, 12, 10, 14, 10, 8, 22171, 9, 10, 7, 13, 7, 8, 7, 8, 11, 11, 9, 8, 12, 10, 9, 11, 14, 10, 8, 6, 10, 7, 5, 8, 13, 9, 11, 10, 2, 11, 8, 5, 10, 12, 9, 10, 9, 10, 8, 7, 7, 10, 11, 11, 7, 10, 10, 8, 13, 7, 11, 7, 8, 10, 11, 7, 10, 8, 9, 6, 6, 10, 11, 8, 11, 7, 10, 11, 11, 8, 9, 8, 12, 8, 8, 10, 12, 9, 7, 7, 10, 11, 13, 9, 13, 9, 6, 8, 8, 11, 8, 11, 12, 13, 9, 7, 7, 10, 10, 10, 5, 5, 10, 790918, 6, 7, 9, 8, 13, 10, 2, 7, 10, 9, 11, 9, 6, 8, 40328, 11, 12, 10, 5, 7, 9, 9, 11, 8, 8, 8, 9, 5, 7, 7, 7, 12, 12, 11, 14, 9, 12316024, 10, 10, 4, 5, 10, 8, 11, 8, 9, 8, 12, 12, 8, 12, 9, 6, 9, 8, 3, 8, 10, 9, 10, 9, 12, 8, 9, 3, 10, 4, 10, 6, 8, 11, 25542, 8, 13, 3601434, 9, 10, 8}

Returns: {-1 }
{10, 13, 9, 8, 11, 11, 6, 9, 7, 7, 10, 8, 11, 8, 8, 10, 12, 6, 10, 10, 12, 6, 8, 11, 10, 5, 8, 12, 17, 11, 12, 12, 8, 13, 12, 14, 6, 123361, 8, 7, 14, 7, 11, 12, 14, 13, 11, 11, 6, 9, 12, 4, 9, 11, 10, 9, 13, 5, 10, 12, 10, 7, 8, 10, 8, 9, 12, 14, 6, 9, 5, 5, 9, 10, 3, 11, 4, 9, 7, 12, 10, 10, 5, 12, 9, 5, 9, 11, 10, 12, 8, 10, 15, 8, 12, 10, 13, 7, 9, 11, 10, 8, 6, 10, 6, 14, 11, 13, 15, 11, 6, 11, 13, 13, 10, 4, 13, 9, 7, 14, 11, 12, 11, 10, 11, 9, 14, 9, 12, 6, 7, 9, 12, 9, 8, 9, 12, 11, 10, 8, 12, 9, 5, 11, 15, 13, 11, 10, 10, 10, 11, 11, 6, 12, 11, 6, 13, 10, 10, 9, 8, 6, 8, 6, 11, 6, 7, 9, 5, 17, 6, 13, 9, 6, 9, 6, 8, 10, 4, 12, 11, 11, 7, 7, 7, 7, 6, 11, 10, 8, 9, 10, 11, 11, 9, 9, 6, 10, 6, 11, 9, 7, 8, 6, 11, 15, 10, 13, 13, 11, 10, 7, 10, 6, 8, 9, 6, 9, 12, 8, 7, 5, 11, 16, 9, 11, 6, 11, 6, 14, 12, 6, 12, 11, 15, 5, 9, 14, 6, 12, 9, 14, 9, 9, 8, 13, 7, 5, 12, 7, 7, 11, 3, 14, 10, 16, 6, 13, 13, 10, 7, 6, 7, 10, 7, 12, 14, 6, 6, 11, 12, 11, 14, 8, 8, 14, 10, 11, 9, 6, 5, 7, 10, 12, 8, 16, 14, 11, 3, 11, 8, 8, 8, 11, 13, 8, 8, 13, 15, 6, 6, 6, 15, 10, 15, 11, 10, 9, 9, 10, 14, 8, 8, 5, 8, 10, 6, 5, 15, 6, 11, 10, 12, 12, 11, 9, 5, 11, 6, 11, 10, 11, 9, 11, 12, 6, 10, 13, 12, 10, 16, 13, 6, 13, 14, 13, 12, 12, 5, 9, 10, 13, 10, 12, 11, 10, 9, 15, 9, 7, 10, 11, 12, 9, 13, 13, 13, 14, 12, 5, 9, 5, 17, 11, 8, 6, 4, 6, 11, 11, 8, 14, 10, 14, 12, 6, 10, 11, 10, 13, 11, 12, 7, 11, 10, 10, 5, 8, 8, 13, 11, 8, 15, 10, 8, 8, 9, 12, 11, 4, 8, 2, 9, 8, 12, 11, 5, 15, 8, 13, 11, 12, 7, 6, 8, 9, 15, 8, 10, 10, 11, 8, 6, 13, 9, 6, 8, 13, 9, 5, 10, 9, 11, 11, 10, 12, 10, 11, 13, 9, 13, 12, 12, 10, 50486, 12, 9, 8, 8, 13, 10, 9, 9, 16, 9, 10, 6, 11, 4, 6, 15, 7, 15, 8, 11, 12, 8, 9, 7, 11, 10, 4, 9, 5, 14, 10, 10, 7, 13, 7, 13, 9, 9, 12, 8, 5, 8, 7, 12, 9, 4, 12, 7, 6, 10, 6, 8, 10, 13, 11, 9, 10, 11, 7, 7, 13, 10, 10, 6, 12, 10, 14, 11, 7, 12, 10, 8, 7, 14, 8, 8, 12, 10, 11, 10, 7, 11, 4, 11, 13, 9, 5, 6, 8, 14, 12, 6, 13, 6, 13, 10, 10, 12, 11, 16, 9, 7, 12, 9, 8, 6, 11, 11, 10, 5, 12, 12, 15, 7, 15, 6, 12, 6, 10, 11, 6, 10, 16, 8, 11, 13, 3, 4, 5, 9, 7, 12, 13, 9, 12, 5, 7, 6, 8, 11, 7, 11, 9, 5, 9, 13, 10, 10, 10, 10, 10, 12, 9, 7, 14, 12, 8, 12, 13, 11, 6, 14, 11, 10, 7, 11, 9, 11, 5, 6, 7, 16, 10, 9, 10, 8, 9, 8, 5, 13, 8, 5, 12, 15, 12, 11, 14, 13, 9, 8, 13, 13, 9, 5, 11, 6, 5, 5, 8, 12, 6, 6, 6, 11, 9, 11, 13, 5, 6, 11, 13, 6, 6, 11, 10, 11, 13, 5, 10, 7, 12, 15, 11, 8, 7, 8, 16, 5, 14, 11, 16, 10, 9, 7, 11, 14, 10, 10, 10, 11, 7, 10, 8, 16, 10, 5, 8, 10, 10, 13, 10, 12, 12, 7, 8, 9, 10, 8, 5, 7, 6, 10, 7, 2, 11, 9, 6, 15, 7, 9, 12, 8, 12, 13, 10, 8, 13, 11, 6, 7, 7, 11, 10, 8, 9, 11, 10, 6, 9, 8, 5, 8, 5, 13, 6, 13, 12, 10, 9, 11, 5, 9, 10, 5, 6, 5, 9, 12, 6, 13, 7, 7, 6, 12, 11, 12, 12, 10, 11, 11, 6, 15, 12, 11, 8, 12, 5, 6, 9, 9, 9, 8, 7, 8, 6, 11, 12, 7, 8, 7, 5, 12, 10, 12, 6, 8, 10, 8, 12, 8, 12, 9, 8, 10, 12, 10, 9, 11, 5, 13, 10, 6, 7, 5, 8, 12, 11, 9, 9, 12, 6, 14, 9, 11, 7, 9, 10, 7, 14, 7, 11, 10, 10, 8, 9, 5, 4, 12, 8, 13, 10, 10, 11, 13, 7, 9, 6, 10, 13, 12, 4, 5, 10, 13, 5, 7, 11, 15, 8, 12, 8, 15, 11, 10, 9, 7, 16, 8, 13, 12, 9, 9, 10, 9, 10, 6, 11, 6, 13, 13, 11, 10, 14, 6, 6, 11, 10, 11, 7, 16, 9, 6, 14, 14, 9, 11, 8, 11, 10, 15, 8, 10, 11, 6, 8, 15, 10, 13, 11, 11, 5, 9, 4, 13, 11, 13, 7, 7, 8, 10, 8, 9, 9, 7, 9, 11, 206818, 6, 9, 13, 12, 9, 5, 10, 11, 7, 9, 14, 11, 16, 7, 8, 13, 11, 11, 12, 11, 6, 13, 9, 12, 10, 6, 9, 6, 6, 12, 11, 6, 12, 10, 12, 13, 6, 10, 11, 12, 5, 11, 10, 11, 3, 11, 8, 11, 10, 13, 11, 13, 13, 7, 12, 5, 9, 8, 10, 7, 10, 7, 7, 11, 8, 12, 14, 8}

Returns: {-1 }
{7, 9, 11, 6, 8, 9, 8, 11, 9, 8, 11, 9, 6, 7, 8, 5, 11, 8, 11, 9, 12, 12, 8, 9, 7, 8, 5, 10, 9, 10, 11, 6, 8, 6, 14, 8, 12, 10, 9, 8, 6, 11, 14, 8, 12, 10, 12, 6, 9, 10, 9, 7, 12, 12, 8, 6, 6, 8, 10, 9, 5, 6, 8, 10, 13, 11, 7, 7, 9, 8, 10, 7, 7, 11, 11, 4, 15, 8, 15, 7, 8, 11, 7, 12, 6, 9, 8, 6, 6, 9, 10, 7, 7, 9, 12, 9, 9, 8, 11, 8, 10, 10, 12, 5481, 10, 10, 10, 15, 13, 8, 8, 8, 5, 10, 7, 9, 11, 9, 9, 14, 259275883, 7, 7, 7, 8, 7, 8, 11, 10, 7, 9, 10, 6, 8, 7, 10, 8, 9, 13, 10, 8, 7, 9, 10, 11, 10, 7, 12, 9, 9, 11, 9, 7, 8, 7, 11, 3, 3, 11, 6, 13, 14, 13, 5, 7, 4, 11, 8, 6, 12, 5, 5, 7, 10, 6, 9, 5, 11, 8, 7, 6, 8, 9, 10, 11, 8, 9, 12, 5, 14, 7, 14, 15, 8, 7, 6, 6, 8, 15, 14, 11, 9, 10, 15, 10, 8, 7, 6, 11, 6, 15, 10, 8, 10, 10, 5, 11, 7, 3742, 8, 6, 8, 8, 8, 9, 6, 9, 6, 10, 11, 13, 9, 9, 12, 7, 81957982, 6, 5, 10, 8, 8, 9, 15, 8, 7282552, 7, 7, 11, 15, 8, 7, 4, 15, 5, 9, 8, 7, 14, 8, 8, 9, 8, 5, 10, 7, 5, 9, 6, 5, 11, 14, 8, 5, 12, 10, 3, 9, 10, 8, 9, 9, 8, 5, 10, 10, 7, 6, 11, 10, 15, 9, 9, 8, 7, 12, 9, 9, 8, 5, 8, 10, 12, 11, 15, 10, 11, 11, 6, 8, 8, 11, 12, 6, 10, 12, 10, 9, 11, 9, 9, 11, 7, 12, 12, 7, 8, 10, 8, 8, 13, 6, 12, 7, 10, 9, 10, 9, 5, 7, 7, 6, 15, 9, 10, 6, 12, 9, 13, 8, 7, 7, 8, 4, 8, 9, 6, 7, 8, 7, 8, 9, 6, 4, 8, 6, 5, 15, 7, 8, 7, 8, 7, 12, 11, 7, 8, 10, 5, 8, 15, 9, 5, 10, 11, 8, 15, 8, 5, 10, 8, 9, 9, 8, 222068, 8, 6, 8, 15, 6, 10, 9, 11, 7, 9, 9, 9, 11, 9, 9, 11, 7, 10, 11, 6, 12, 3, 11, 5, 8, 9, 8, 9, 7, 12, 8, 7, 5, 13, 8, 8, 8, 12, 9, 8, 8, 9, 9, 10, 7, 8, 4, 7, 9, 13, 11, 6, 10, 11, 8, 5, 14, 7, 13, 12, 8, 8, 11, 10, 8, 8, 6, 8, 6, 8, 6, 13, 7, 15, 11, 12, 8, 8, 12, 7, 10, 12, 7, 11, 32702, 5, 13, 6, 14, 9, 5, 7, 8, 11, 6, 9, 8, 14, 7, 8, 6, 6, 4, 14, 8, 11, 8, 9, 10, 9, 6, 8, 12, 7, 7, 8, 7, 9, 7, 10, 8, 6, 6, 12, 8, 4, 7, 4, 12, 9, 12, 11, 12, 4, 7, 6, 8, 7, 13, 8, 12, 8, 10, 7, 9, 7, 11, 8, 13, 9, 13, 11, 8, 10, 8, 5, 11, 14, 10, 6, 8, 9, 7, 9, 5, 9, 8, 3470, 13, 10, 9, 11, 8, 8, 15, 10, 12, 13, 5, 23449, 9, 14, 9, 7, 12, 12, 10, 5, 9, 9, 12, 7, 8, 9, 7, 10, 6, 8, 8, 8, 12, 5, 11, 7, 14, 8, 8, 10, 8, 9, 7968, 13, 12, 7, 10, 8, 7, 8, 9, 9, 9, 11, 5, 8, 7, 7, 7, 8, 7, 9, 8, 9, 7, 12, 5, 6, 8, 11, 9, 15, 10, 4, 8, 8, 4, 8, 11, 8, 8, 12, 7, 10, 5, 9, 14, 9, 10, 12, 9, 3, 11, 15, 7, 6, 9, 13, 11, 7, 6, 9, 8, 11, 8, 8, 8, 9, 5, 14, 8, 12, 8, 5, 8, 8, 12, 13, 8, 12, 9, 13, 8, 10, 9, 8, 6, 13, 12, 7, 9, 13, 8, 9, 8, 6, 8, 11, 13, 10, 10, 7, 6, 5, 8, 6, 13, 7, 14, 12, 8, 9, 8, 5, 10, 11, 8, 7, 8, 8, 7, 10, 10, 7, 9, 10, 9, 7, 10, 8, 12, 8, 13, 8, 7, 10, 11, 12, 7876, 10, 6, 6, 8, 10, 13, 4, 11, 8, 8, 6, 5, 12, 11, 7, 8, 135345, 6, 12, 8, 5, 11, 7, 12, 11, 8, 9, 10, 8, 7, 14, 14, 8, 8, 11, 9, 6, 10, 5, 8, 8, 7, 12, 9, 8, 10, 10, 7, 8, 13, 9, 8, 5, 6, 5, 10, 8, 14, 5, 9, 13, 8, 4, 9, 5, 7, 2, 14, 9, 11, 2371, 10, 15, 9, 11, 4, 13, 5, 11, 7, 9, 11, 8, 8, 10, 6, 8, 7, 12, 10, 10, 12, 9, 9, 9, 11, 8, 11, 6, 12, 9, 5, 11, 12, 11, 6, 8, 6, 10, 13, 7, 11, 9, 6, 8, 11, 8, 8, 4, 8, 5, 13, 7, 8, 8, 6, 12, 8, 7, 4, 15, 10, 12, 11, 11, 8, 12, 10, 9, 9, 9, 12, 10, 11, 8, 6, 12, 11, 8, 14, 11, 9, 10, 8, 5, 5, 6, 7, 6, 6, 5, 8, 8, 6, 4, 8, 11, 6, 8, 9, 7, 7, 10, 10, 4, 13, 9, 11, 7, 9, 12, 9, 10, 8, 10, 8, 14, 10, 9, 8, 10, 7, 9, 9, 13, 9, 14, 14, 10, 8, 10, 15, 7, 13, 5, 9, 8, 8, 9, 6, 11, 12, 8, 11, 8, 318329281, 12, 11, 9, 8, 12, 14, 6, 5, 7, 6, 5, 3, 9, 11, 12, 446186, 8, 10, 284072, 7}

Returns: {-1 }
{8, 9, 10, 499306813, 6, 7, 10, 10, 5, 9, 15, 10, 11, 10, 10, 9, 10, 9, 9, 14, 11, 7, 8, 15, 10, 6, 8, 13, 12, 12, 8, 10, 9, 3, 11, 10, 11, 11, 10, 10, 11, 9, 4, 8, 4, 10, 12, 13, 3, 8, 10, 9, 6, 11, 12, 9, 13, 7, 12, 9, 9, 3, 11, 7, 9, 8, 8, 7, 10, 9, 11, 10, 63590, 9, 10, 12, 8, 14, 10, 7, 4, 9, 11, 7, 10, 9, 8, 7, 5, 6, 13, 8, 6, 6, 7, 8, 10, 7, 12, 7, 10, 7, 11, 10, 7, 13, 9, 8, 10, 10, 8, 10, 7, 7, 10, 7, 8, 10, 12, 8, 11, 5, 11, 9, 8, 9, 20624554, 10, 9, 10, 6, 8, 8, 10, 12, 10, 12, 9, 10, 11, 4, 14, 7, 14, 12, 9, 11, 4, 8, 13, 9, 9, 9, 10, 13, 10, 7, 9, 11, 12, 191824404, 36673, 8, 8, 12, 7, 7, 5, 8, 10, 9, 12, 8, 9, 8, 8, 8, 6, 10, 11, 10, 8, 12, 8, 8, 8, 6, 6, 8, 3, 13, 11, 8, 7, 8, 7, 9, 12, 9, 13, 9, 7, 10, 11, 11, 12, 10, 5, 7, 9, 7, 6, 7, 7, 12, 9, 9, 4, 9, 7, 10, 9, 8, 10, 6, 8, 10, 11, 7, 7, 9, 9, 6, 4, 8, 8, 10, 8, 5, 10, 6, 10, 5, 9, 8, 5, 7, 10, 8, 10, 13, 10, 7, 10, 8, 6, 8, 9, 10, 12, 9, 12, 10, 13, 9, 9, 13, 9, 8, 10, 8, 10, 9, 10, 8, 261217, 13, 8, 10, 11, 14, 9, 12, 11, 8, 10, 8, 6, 9, 8, 8, 11, 10, 6, 14, 8, 9, 13, 6, 8, 7, 8, 6, 11, 10, 8, 8, 10, 10, 9, 8, 7, 13, 7, 7, 8, 11, 141654, 7, 6, 7, 12, 14, 8, 7, 14, 9, 8, 9, 4, 11, 95837, 9, 6, 8, 6, 6, 8, 9, 9, 10, 13, 8, 13, 9, 12, 7, 13, 11, 10, 5, 10, 11, 14, 5, 6, 9, 7, 11, 8, 5, 7, 11, 12, 7, 6, 10, 3, 9, 10, 7, 9, 9, 8, 7, 10, 7, 7, 13, 9, 7, 7, 5, 8, 10, 14, 12, 11, 6, 6, 10, 7, 8, 7, 13, 6, 9, 14, 11, 8, 10, 8, 13, 12, 1327577, 8, 9, 11, 9, 9, 13, 8, 12, 9, 4, 4, 13, 7, 9, 15, 14, 8, 12, 5, 9, 5, 5, 11, 10, 8, 9, 10, 6, 12, 9, 8, 10, 8, 9, 7, 9, 10, 7, 11, 12, 13, 13, 7, 10, 12, 12, 13, 7, 10, 8, 9, 12, 7, 13, 13, 11, 8, 9, 9, 5, 9, 5, 8, 8, 6, 9, 9, 10, 9, 6, 6, 10, 13, 10, 7, 7, 9, 13, 12, 13, 8, 1575, 14, 7, 6, 11, 8, 13, 13, 11, 8, 5, 10, 6174498, 8, 8, 9, 8, 9, 7, 10, 9, 7, 6, 9, 9, 10, 12, 5, 11, 8, 5, 7, 11, 8, 10, 7, 8, 10, 13, 11, 9, 7, 9, 9, 13, 11, 10, 7, 7, 7, 7, 6, 7, 9, 9, 9, 9, 773744, 6, 10, 6, 8, 13, 8, 10, 7, 8, 7, 9, 9, 9, 10, 8, 9, 5, 10, 13, 5, 13, 13, 6, 10, 7, 9, 9, 10, 8, 9, 9, 11, 221407, 13, 11, 8, 11, 10, 11, 8, 8, 12, 10, 6, 8, 7, 8, 9, 9, 11, 10, 10, 9, 6, 6, 7, 6, 4, 8, 13, 12, 10, 12, 12, 10, 10, 6, 10, 8, 10, 7, 8, 8, 9, 10, 12, 12, 10, 6, 7, 11, 9, 55907026, 8, 6, 11, 13, 13, 5, 6, 8, 12, 10, 11, 8, 9, 11, 9, 12, 7, 7, 9, 10, 8, 8, 8, 47690, 9, 6, 3, 10, 8, 7, 9, 11, 6, 11, 8, 11, 9, 13, 8, 8, 12, 10, 6, 5, 9, 9, 11, 9, 7, 9, 9, 5, 5, 14, 10, 9, 11, 11, 13, 8, 13, 12, 9, 9, 13, 6, 11, 13, 11, 7, 9, 9, 7, 8, 3, 9, 10, 8, 220586228, 6, 7, 9, 8, 12, 8, 12, 7, 8, 12, 11, 13, 12, 6, 13, 10, 7, 2, 6, 10, 5, 7, 12, 11, 12, 12, 9, 9, 10, 11, 12, 12, 8, 8, 11, 6, 13, 3, 9, 3, 6, 5, 8, 5, 9, 7, 10, 14, 7, 7, 6, 193501, 13, 6, 10, 10, 9, 8, 13, 10, 12, 6, 11, 12, 6, 10, 5, 7, 8, 7, 9, 7, 8, 7, 6, 4, 8, 7, 10, 9, 12, 4, 9, 7, 11, 9, 9, 6, 9, 8, 7, 8, 13, 7, 7, 11, 5, 9, 10, 5, 12, 8, 8, 11, 8, 6, 9, 11, 236850047, 9, 11, 5, 5, 5, 10, 6, 10, 9, 9, 13, 10, 11, 10, 7, 10, 7, 10, 5, 10, 10, 7, 9, 9, 12, 6, 6, 11, 8, 10, 10, 9, 7, 8, 11, 12, 9, 10, 11, 12, 8, 4, 7, 8, 8, 7, 10, 10, 4, 13, 9, 7, 11, 10, 6, 14, 13, 9, 12, 8, 8, 9, 11, 12, 8, 8, 11290, 8, 9, 11, 13, 8, 6, 10, 12, 13, 6, 10, 14, 9, 6, 9, 8, 14, 12, 6, 10, 7, 9, 7, 12, 8, 12, 8, 9, 12, 13, 8, 10, 9, 14, 7, 12, 9, 12, 10, 8, 10, 8, 9, 8, 5, 10, 9, 9, 7, 7, 8, 7, 9, 12, 10, 12, 9, 14, 13, 12, 5, 8, 5, 5, 9, 10, 11, 5, 8, 12, 8, 5, 8, 9, 9, 8, 7, 13, 6, 6, 12, 10, 5, 9, 11, 9, 8, 5, 11, 9, 10, 9, 11, 10, 9, 6, 9, 8, 13, 10, 12, 8, 7, 7, 12, 13, 12, 11, 13, 7, 9, 12, 8, 7}

Returns: {-1 }
{3, 13, 11, 5, 7, 7, 12, 6, 14, 11, 8, 6, 8, 13, 8, 9, 7, 5, 7, 11, 5, 12, 7, 5, 4, 7, 8, 14, 11, 7, 9, 11, 6, 6, 10, 8, 8, 8, 5, 8, 10, 5, 8, 10, 9, 10, 7, 8, 6, 5, 7, 13, 10, 9, 9, 10, 12, 6, 5, 7, 10, 7, 12, 6, 10, 11, 11, 11, 11, 11, 4, 6, 9, 12, 8, 5, 12, 10, 6, 11, 6, 9, 9, 6, 5, 12, 7, 10, 12, 10, 9, 12, 9, 12, 7, 6, 6, 7, 6, 8, 6, 11, 11, 11, 5, 7, 6, 11, 10, 6, 5, 9, 5, 10, 11, 9, 9, 7, 12, 4, 9, 7, 11, 11, 12, 8, 7, 11, 15, 5, 12, 9, 5, 8, 12, 6, 9, 12, 5, 6, 5, 8, 9, 10, 10, 6, 9, 9, 12, 11, 8, 9, 7, 5, 11, 6, 8, 15, 10, 10, 7, 5, 11, 7, 6, 8, 8, 7, 9, 6, 13, 8, 8, 10, 12, 9, 7, 12, 8, 11, 12, 10, 7, 11, 9, 12, 8, 12, 14, 7, 5, 8, 8, 9, 11, 10, 8, 7, 11, 10, 11, 9, 6, 10, 3, 4, 11, 10, 16469480, 10, 11, 6, 5, 5, 11, 7, 11, 6, 7, 9, 7, 9, 5, 11, 7, 9, 4, 7, 11, 9, 8, 10, 11, 12, 10, 9, 11, 10, 5, 6, 8, 11, 5, 5, 5, 11, 4, 6, 7, 10, 7, 9, 10, 11, 6, 11, 6, 7, 6, 10, 8, 10, 6, 5, 11, 10, 10, 11, 5, 6, 9, 10, 12, 6, 11, 7, 11, 8, 7, 10, 11, 10, 8, 8, 10, 9, 6, 6, 6, 8, 10, 5, 9, 11, 8, 8, 11, 13, 8, 11, 11, 6, 6, 10, 12, 9, 12, 9, 7, 5, 8, 10, 9, 8, 12, 11, 7, 7, 12, 6, 10, 9, 11, 8, 10, 10, 11, 13, 7, 8, 8, 8, 8, 6, 5, 10, 7, 12, 5, 5, 9, 5, 6, 12, 7, 11, 5, 11, 6, 10, 8, 5, 8, 7, 8, 11, 10, 6, 6, 4, 7, 10, 8, 5, 10, 9, 4, 13, 10, 6, 8, 10, 6, 13, 11, 7, 8, 9, 10, 10, 6, 7, 5, 8, 11, 8, 5, 5, 11, 9, 13, 9, 12, 9, 3, 7, 5, 6, 6, 13, 10, 11, 5, 6, 11, 13, 8, 9, 11, 7, 6, 9, 8, 6, 12, 8, 6, 11, 7, 4, 10, 8, 10, 7, 9, 3, 12, 4, 5, 12, 10, 12, 11, 11, 6, 13, 8, 11, 8, 10, 7, 11, 10, 10, 7, 11, 5, 4, 12, 10, 6, 6, 8087214, 9, 9, 10, 10, 11, 7, 7, 6, 9, 5, 12, 9, 11, 9, 12, 10, 11, 9, 10, 9, 13, 8, 9, 10, 10, 11, 6, 7, 5, 8, 9, 7, 8, 6, 6, 6, 6, 7, 7, 7, 9, 8, 6, 7, 9, 10, 11, 4, 4, 9, 10, 8, 10, 5756032, 10, 11, 6, 11, 7, 8, 12, 10, 4, 11, 10, 5, 7, 12, 8, 7, 9, 10, 9, 13, 15, 6, 7, 5, 8, 11, 12, 10, 9, 11, 12, 4, 9, 11, 10, 7, 9, 6, 7, 10, 11, 7, 6, 5, 13, 11, 10, 12, 10, 10, 10, 7, 9, 8, 5, 7, 6, 9, 8, 10, 8, 8, 7, 13, 11, 10, 10, 5, 11, 12, 11, 12, 12, 9, 4, 14, 6, 9, 8, 8, 6, 11, 10, 8, 6, 6, 11, 6, 10, 11, 12, 8, 10, 12, 6, 7, 5, 9, 12, 7, 9, 10, 7, 8, 9, 14, 7, 12, 6, 11, 10, 9, 12, 8, 10, 7, 10, 10, 3, 7, 11, 7, 10, 10, 8, 9, 7, 7, 6, 9, 13, 9, 8, 11, 5, 10, 11, 8, 6, 11, 7, 9, 12, 7, 12, 10, 7, 7, 5, 11, 10, 9, 13, 10, 11, 9, 9, 9, 10, 7, 5, 11, 8, 6, 8, 6, 9, 9, 9, 10, 8, 7, 10, 7, 12, 8, 9, 6, 7, 8, 7, 5, 6, 11, 10, 7, 12, 8, 7, 11, 8, 11, 9, 7, 8, 9, 7, 12, 9, 8, 10, 5, 5, 12, 6, 12, 14, 9, 13, 9, 11, 9, 11, 11, 7, 6, 6, 12, 6, 12, 9, 8, 10, 102524, 12, 10, 8, 10, 9, 7, 8, 12, 5, 6, 12, 7, 8, 7, 9, 10, 13, 10, 8, 13, 12, 7, 13, 12, 6, 6, 9, 8, 10, 8, 5, 8, 9, 11, 7, 10, 7, 6, 8, 8, 6, 9, 6, 5, 8, 12, 6, 10, 8, 10, 10, 9, 6, 9, 8, 11, 6, 13, 7, 8, 5, 13, 10, 12, 7, 3, 7, 13, 10, 10, 10, 12, 9, 7, 9, 10, 6, 9, 11, 12, 9, 6, 13, 5, 8, 10, 7, 6, 8, 11, 13, 8, 7, 5, 12, 10, 9, 10, 12, 12, 9, 10, 9, 11, 3806901, 6, 3478, 12, 11, 12, 5, 8, 6, 9, 5, 9, 9, 11, 10, 12, 9, 8, 8, 11, 8, 12, 10, 5, 12, 12, 7, 7, 10, 12, 11, 7, 10, 8, 13, 9, 7, 11, 11, 8, 8, 9, 11, 6, 6, 7, 5, 6, 10, 5, 11, 7, 8, 6, 10, 8, 8, 12, 7, 6, 8, 6, 13, 5, 8, 11, 7, 10, 9, 11, 10, 6, 7, 5, 11, 5, 5, 5, 10, 14, 8, 13, 10, 5, 8, 8, 10, 14, 9, 12, 9, 8, 7, 6, 13, 8, 13, 5, 11, 13, 9, 5, 14, 10, 5, 12, 13, 7, 12, 8, 7, 9, 10, 10, 8, 5, 7, 7, 6, 14, 12, 6, 8, 9, 10, 5, 11, 5, 10, 9, 12, 6, 10, 14, 11, 10, 11, 8, 11, 8, 9, 9, 7, 6, 9, 14, 12, 14, 7, 6, 10, 6, 14, 7, 6, 9, 8, 12, 7, 10}

Returns: {0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{12, 12, 15, 6, 10, 7, 9, 6, 8, 11, 6, 5, 4, 6, 10, 9, 9, 8, 9, 8, 10, 7, 9, 13, 5, 8, 10, 6, 8, 10, 13, 10, 9, 12, 5, 6, 10, 8, 5, 8, 13, 10, 9, 9, 13, 7, 8, 7, 11, 10, 8, 10, 10, 8, 8, 7, 7, 5, 12, 12, 11, 8, 11, 8, 8, 4, 8, 9, 6, 6, 12, 8, 12, 8, 12, 11, 12, 7, 8, 6, 10, 9, 6, 6, 7, 5, 11, 8, 9, 9, 8, 8, 5, 13, 11, 8, 6, 7, 7, 6, 8, 12, 13, 7, 6, 9, 8, 12, 13, 12, 11, 6, 12, 10, 6, 7, 7, 11, 7, 5, 7, 8, 8, 13, 8, 5, 6, 12, 10, 6, 7, 12, 10, 13, 7, 11, 7, 7, 7, 9, 12, 8, 10, 14, 3, 12, 9, 8, 11, 12, 5, 12, 13, 7, 7, 12, 12, 8, 7, 9, 9, 8, 10, 6, 8, 5, 11, 11, 7, 6, 10, 8, 7, 10, 9, 10, 6, 7, 10, 7, 8, 6, 7, 9, 7, 8, 9, 10, 9, 10, 10, 12, 8, 8, 10, 8, 10, 13, 8, 9, 9, 7, 11, 7, 9, 8, 10, 7, 7, 8, 13, 7, 11, 6, 9, 13, 6, 13, 7, 8, 8, 6, 6, 12, 9, 10, 11, 8, 11, 9, 9, 11, 9, 9, 6, 6, 8, 9, 8, 8, 9, 11, 6, 6, 14, 6, 10, 6, 9, 3, 8, 8, 10, 7, 11, 12, 7, 11, 10, 9, 9, 7, 9, 11, 7, 11, 8, 10, 13, 11, 8, 9, 962797, 10, 6, 6, 4, 12, 10, 10, 6, 13, 7, 9, 4, 12, 10, 9, 8, 8, 7, 13, 9, 10, 9, 7, 5, 12, 10, 9, 10, 14, 11, 8, 3, 8, 10, 6, 10, 6, 7, 7, 5, 11, 11, 14, 7, 8, 7, 8, 9, 6, 6, 6, 8, 11, 9, 13, 6, 9, 6, 9, 8, 9, 8, 7, 6, 5, 12, 7, 7, 13, 13, 7, 4, 4, 6, 8, 13, 11, 13, 10, 10, 7, 10, 8, 5, 11, 6, 8, 6, 11, 7, 8, 8, 12, 8, 8, 10, 10, 7, 13, 9, 13, 7, 7, 13, 5, 6, 8, 10, 5, 8, 5, 9, 10, 11, 10, 6, 11, 6, 10, 10, 4, 13, 7, 11, 7, 12, 5, 13, 7, 9, 11, 12, 4, 10, 14, 6, 6, 7, 42250088, 10, 7, 10, 12, 8, 10, 9, 10, 10, 6, 10, 13, 6, 4, 10, 5, 6, 8, 12, 5, 9, 6, 13, 13, 12, 9, 8, 11, 6, 7, 5, 5, 8, 6, 10, 5, 8, 7, 8, 8, 12, 5, 9, 9, 5, 5, 10, 7, 5, 9, 9, 7, 7, 4, 6, 10, 10, 5, 6, 9, 11, 6, 11, 6, 9, 13, 7, 10, 5, 7, 10, 8, 8, 11, 11, 7, 8, 12, 11, 6, 9, 10, 11, 13, 7, 6, 6, 11, 9, 10, 11, 8, 10, 11, 13, 7, 8, 11, 11, 10, 12, 9, 2, 13, 12, 6, 12, 12, 10, 9, 10, 8, 10, 12, 10, 7, 11, 9, 13, 5, 7, 13, 9, 5, 5, 8, 12, 6, 6, 11, 11, 6, 12, 9, 7, 6, 10, 12, 10, 5, 7, 13, 9, 12, 11, 8, 5, 8, 12, 9, 5, 7, 9, 8, 6, 9, 9, 13, 13, 6, 3, 15, 9, 10, 9, 8, 7, 9, 11, 9, 5, 7, 5, 6, 8, 8, 7, 6, 8, 14, 8, 10, 8, 7, 7, 11, 4, 8, 11, 7, 11, 13, 6, 11, 10, 9, 13, 9, 9, 6, 9, 7, 8, 8, 6, 13, 6, 10, 8, 9, 7, 7, 6, 6, 12, 10, 10, 11, 11, 5, 7, 11, 12, 10, 9, 12, 6, 7, 8, 7, 8, 12, 8, 12, 5, 9, 13, 6, 10, 10, 5, 5, 12, 7, 12, 4, 7, 13, 13, 11, 6, 8, 10, 8, 6, 10, 8, 12, 13, 8, 14, 11, 9, 13, 13, 10, 9, 12, 11, 7, 12, 7, 15, 13, 12, 7, 11, 5, 8, 9, 11, 6, 10, 7, 8, 4, 12, 9, 6, 7, 9, 11, 6, 12, 5, 11, 8, 10, 7, 8, 10, 8, 10, 8, 11, 7, 5, 10, 12, 6, 11, 7, 8, 8, 5, 13, 8, 6, 6, 8, 6, 9, 7, 7, 12, 9, 8, 6, 11, 5, 10, 4, 7, 8, 4, 9, 9, 11, 9, 13, 13, 10, 8, 10, 6, 7, 8, 6, 11, 10, 9, 12, 11, 11, 8, 9, 13, 10, 8, 10, 8, 13, 12, 11, 8, 7, 12, 9, 10, 7, 11, 7, 7, 4, 6, 6, 14, 9, 6, 12, 5, 8, 10, 10, 6, 11, 11, 11, 9, 12, 9, 7, 8, 11, 10, 9, 8, 7, 4, 10, 6, 10, 8, 10, 7, 9, 5, 10, 12, 7, 7, 10, 5, 9, 11, 5, 10, 4, 5, 8, 6, 8, 6, 10, 11, 9, 5, 12, 9, 11, 11, 8, 10, 12, 11, 10, 11, 9, 6, 6, 8, 8, 6, 7, 8, 5, 12, 11, 9, 9, 8, 13, 8, 12, 5, 5, 7, 12, 12, 11, 9, 7, 4, 9, 9, 9, 13, 10, 11, 8, 11, 10, 9, 11, 11, 10, 11, 8, 8, 10, 12, 8, 6, 9, 9, 12, 10, 6, 9, 7, 12, 11, 12, 12, 12, 6, 8, 12, 6, 7, 12, 10, 9, 5, 7, 7, 6, 10, 11, 7, 6, 6, 7, 10, 11, 12, 13, 12, 6, 8, 12, 7, 10, 7, 7, 10, 5, 13, 9, 8, 12, 8, 10, 2238109, 8, 10, 7, 11, 7, 7, 12, 8, 10, 11, 10, 11, 5, 7, 10, 10, 8, 9, 7, 7, 12, 6, 9, 6, 10, 8, 10, 10, 9, 7, 9, 13, 8, 10, 5, 9, 11, 8, 6, 11, 7, 6, 6, 8, 8, 8, 5, 6, 11, 7, 6, 6, 13, 11}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{8, 8, 6, 11, 5, 8, 8, 11, 11, 8, 7, 11, 10, 13, 12, 12, 10, 6, 9, 10, 11, 6, 9, 10, 10, 14, 9, 8, 9, 12, 14, 11, 7, 6, 8, 13, 12, 11, 9, 9, 8, 10, 9, 10, 7, 10, 10, 10, 10, 7, 11, 10, 13, 5, 6, 9, 6, 9, 11, 11, 15641, 6, 12, 10, 11, 12, 12, 13, 6, 7, 10, 11, 8, 8, 8, 6, 8, 9, 10, 10, 11, 11, 9, 12, 8, 12, 11, 7, 8, 6, 12, 9, 5, 14, 12, 12, 11, 3, 9, 9, 9, 8, 8, 6, 7, 9, 14, 8, 9, 5, 10, 12, 12, 11, 13, 11, 10, 6, 12, 3, 8, 9, 12, 9, 7, 10, 8, 6, 12, 7, 8, 12, 9, 6, 7, 6, 13, 164636, 9, 11, 9, 8, 8, 14, 9, 7, 14, 12, 9, 7, 196872, 10, 12, 6, 11, 12, 13, 11, 7, 7, 11, 11, 8, 15, 13, 9, 10, 6, 13, 6, 10, 11, 10, 11, 11, 10, 9, 10, 13, 13, 12, 9, 8, 11, 10, 8, 8, 14, 7, 10, 71826, 11, 6, 12, 9, 10, 12, 9, 8, 6, 10, 5, 15, 13, 12, 3, 8, 8, 13, 9, 9, 10, 12, 9, 9, 12, 9, 8, 9, 9, 7, 6, 8, 13, 5, 9, 12, 3, 12, 11, 6, 7, 119510332, 8, 8, 7, 11, 10, 9, 5, 8, 13, 11, 69102, 6, 3, 8, 11, 13, 9, 7, 13, 7, 13, 8, 12, 11, 12, 6, 9, 11, 5, 6, 4, 13, 12, 10, 10, 7, 12, 12, 13, 11, 8, 8, 8, 7, 7, 12, 10, 10, 12, 10, 8, 10, 7, 8, 9, 14, 10, 10, 9, 12, 6, 9, 10, 9, 9, 10, 11, 12, 6, 13, 11, 7, 10, 8, 9, 7, 13, 11, 13, 11, 12, 6, 11, 8, 10, 13, 8, 9, 12, 6, 10, 8, 9, 11, 11, 12, 10, 10, 4, 7, 13, 11, 12, 8, 13, 8, 7, 15, 9, 8, 6, 6, 5, 11, 9, 8, 8, 11, 10, 11, 10, 13, 9, 10, 10, 9, 8, 12, 2, 5, 6, 10, 8, 5, 10, 11, 14, 8, 11, 12, 9, 7, 6, 12, 9, 13, 6, 9, 4, 14, 7, 10, 7, 8, 11, 12, 9, 8, 6, 14, 12, 9, 11, 13, 8, 5, 10, 8, 8, 12, 7, 9, 5, 94880, 6, 6, 9, 9, 9, 11, 11, 9, 8, 11, 6, 12, 8, 13, 5, 9, 13, 11, 9, 10, 8, 12, 13, 11, 10, 11, 8, 14, 6, 13, 8, 9, 14, 10, 10, 8, 8, 11, 12, 8, 15, 9, 7, 7, 7, 8, 13, 11, 10, 8, 8, 12, 6, 11, 11, 11, 10, 12, 8, 15, 7, 5, 9, 8, 10, 7, 10, 10, 8, 10, 6, 10, 6, 8, 13, 11, 9, 14, 11, 8, 10, 10, 13, 7, 11, 10, 13, 7, 12, 11, 11, 10, 9, 10, 10, 11, 13, 11, 9, 9, 5, 6, 6, 11, 3, 13, 9, 9, 11, 14, 3, 8, 11, 8, 10, 8, 12, 10, 10, 13, 10, 9, 11, 11, 9, 6, 13, 11, 6, 9, 12, 7, 10, 15, 11, 11, 8, 10, 10, 10, 13, 12, 10, 8, 11, 10, 13, 9, 11, 10, 5, 13, 2, 5, 13, 10, 11, 8, 13, 5, 9, 8, 13, 9, 12, 8, 7, 8, 9, 12, 8, 8, 8, 8, 11, 11, 11, 6, 9, 10, 1995253, 12, 11, 7, 7, 7, 7, 7, 12, 6, 8, 8, 7, 7, 10, 151532, 11, 12, 12, 13, 6, 8, 12, 9, 12, 13, 11, 11, 14, 9, 10, 15, 11, 10, 12, 4, 11, 6, 13, 13, 11, 7, 10, 13, 7, 7, 9, 11, 15, 9, 11, 10, 7, 13, 8, 11, 10, 9, 12, 12, 9, 7, 11, 9, 12, 4, 9, 11, 10, 8, 13, 7, 12, 13, 9, 11, 7, 10, 12, 8, 8, 11, 7, 10, 13, 10, 8, 5, 7, 11, 8, 5, 8, 10, 9, 9, 13, 12, 11, 12, 7, 10, 14, 11, 11, 7, 12, 11, 9, 10, 8, 7, 11, 8, 13, 11, 10, 11, 10, 14, 14, 13, 10, 7, 104446, 12, 9, 5, 8, 6, 8, 7, 11, 8, 11, 6, 11, 6, 9, 11, 6, 8, 14, 7, 11, 14, 13, 12, 3, 9, 10, 8, 8, 11, 8, 13, 8, 7, 11, 13, 8, 8, 10, 9, 10, 5, 12, 8, 6, 9, 8, 8, 11, 12, 3, 7, 11, 9, 11, 8, 10, 11, 7, 8, 12, 5, 9, 14, 11, 10, 6, 6, 8, 11, 11, 8, 12, 9, 9, 12, 10, 10, 5, 7, 6, 10, 7, 6, 11, 11, 9, 13, 12, 10, 10, 12, 5, 7, 8, 8, 9, 11, 8, 11, 13, 11, 7, 3, 13, 8, 9, 11, 6, 13, 8, 10, 11, 13, 8, 12, 10, 9, 7, 13, 10, 6, 10, 13, 10, 11, 11, 13, 12, 7, 13, 12765, 9, 10, 12, 9, 4220719, 6, 12, 11, 11, 7, 8, 8, 9, 8, 12, 6, 8, 12, 7, 14, 6, 8, 13, 8, 9, 11, 12, 11, 7, 13, 5, 5, 10, 7, 10, 7, 9, 15, 13, 14, 9, 7, 13, 8, 14, 12, 6, 9, 7, 4, 13, 11, 11, 9, 5, 12, 7, 11, 12, 11, 12, 11, 13, 11, 10, 5, 9, 9, 8, 12, 11, 8, 5, 6, 3, 11, 3338618, 12, 11, 8, 11, 5876, 9, 11, 9, 14, 11, 8, 14, 11, 9, 7, 10, 6, 11, 12, 9, 12, 13, 10, 6, 8, 7, 6, 10, 6, 10, 14, 8, 7, 8, 10, 8, 14, 10, 8, 9, 14, 9, 9, 5, 8, 10, 13, 12, 11}

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{11, 13, 8, 11, 5, 10, 7, 13, 12, 11, 933018, 15, 12, 10, 8, 15, 7, 5, 7, 6, 13, 5, 5, 14, 11, 12, 16, 9, 10, 8, 10, 12, 10, 11, 6, 4, 10, 14, 15, 7, 12, 6, 10, 7, 6, 11, 10, 7, 7, 10, 9, 9, 11, 13, 7, 9, 7, 6, 5, 12, 11, 9, 10, 9, 5, 7, 6, 3, 415347529, 9, 7, 8, 9, 10, 10, 9, 8, 9, 9, 11, 10, 7, 6, 5, 9, 7, 8, 12, 7, 8, 10, 14, 8, 9, 8, 10, 9, 10, 6, 7, 8, 11, 5, 7, 5, 11, 10, 10, 9, 10, 6, 10, 10, 13, 11, 10, 10, 8, 13, 13, 11, 10, 11, 7, 14, 11, 12, 14, 10, 9, 8, 10, 7, 14, 4, 12, 11, 8, 9, 6, 8, 10, 8, 13, 10, 7, 10, 12, 9, 5, 5, 9, 9, 6340793, 12, 12, 13, 13, 8, 10, 13, 8, 12, 7, 11, 9, 11, 11, 9, 8, 9, 11, 5, 1642, 13, 11, 6, 4, 4, 4, 10, 15, 3, 7, 6, 7, 5, 10, 14, 9, 12, 14, 12, 6, 4662923, 5, 5, 11, 10, 10, 11, 8, 9, 11, 9, 11, 13, 11, 9, 4, 10, 9, 14, 10, 7, 5, 7, 6, 7813, 10, 7, 10, 6, 9, 10, 14, 10, 10, 1132339, 6, 7, 6, 9, 11, 5, 31199931, 10, 5, 7, 14, 9, 5, 12, 13, 7, 10, 11, 10, 7, 7, 9, 7, 6, 9, 11, 12, 8, 6, 10, 4, 9, 8, 11, 13, 2, 11, 6, 5, 9, 11, 14, 5, 7, 6, 13, 11, 9, 6, 7, 6, 10, 13, 6, 12, 11, 11, 10, 10, 6, 8, 7, 7, 9, 15, 11, 6, 13, 6, 5, 7881, 10, 10, 5, 6, 12, 5, 12, 7, 7, 13, 10, 8, 9, 3, 7, 8298202, 11, 5, 9, 13, 5, 5, 10, 11, 14, 5, 8, 10, 8, 8, 13, 6, 6, 9, 10, 8, 9, 6, 14, 14, 10, 9, 9, 12, 8, 9, 7, 4, 9, 11, 12, 12, 9, 7, 4, 10, 11, 11, 10, 7, 11, 4, 8, 7, 7, 6, 9, 11, 9, 12, 12, 8, 11, 10, 10, 189736, 13, 12, 8, 10, 11, 10, 11, 12, 6, 12, 4, 10, 13, 11, 3, 11, 10, 7, 9, 9, 10, 9, 8, 12, 12, 9, 8, 5, 5, 7, 7, 12, 9, 13, 8, 5, 16, 11, 8, 12, 8, 6, 6, 12, 5, 7, 8, 9, 10, 10, 11, 6, 9, 11, 8, 8, 7, 11, 7, 14, 10, 10, 8, 1417, 6, 7, 8, 9, 7, 4, 8, 8, 10, 6, 7, 9, 6, 6, 353217, 12, 7, 7, 8, 8, 6, 114547365, 7, 8, 14, 13, 1096, 9, 9, 8, 9, 11, 10, 7, 8, 5, 13, 13, 16, 14, 8, 10, 8, 13, 7, 11, 11, 5, 6, 15, 6, 14, 9, 11, 11, 6, 8, 13, 6, 15, 11, 15, 15, 7, 11, 7, 12, 8, 6, 8, 6, 7, 8, 6, 8, 286032636, 11, 4, 4, 4, 12, 3889, 8, 14, 12, 7, 11, 11, 13, 10, 11, 14, 11, 7, 13, 10, 11, 11, 14, 7, 11, 14, 8, 11, 4, 10, 9, 12, 9, 13, 7, 11, 11, 11, 13, 11, 11, 13, 7, 10, 8, 8, 8, 10, 12, 14, 12, 14, 7, 7, 8, 12, 10, 7, 5, 10, 10, 16, 12, 12, 11, 7, 8, 8, 8, 10, 6, 10, 13, 8, 13, 10, 4, 8, 4, 6, 12, 16, 7, 5, 7, 9, 14, 7, 12, 4, 10, 8, 7, 8, 11, 13, 10, 9, 8, 9, 12, 5, 12, 13, 6, 11, 7, 11, 9, 15, 12, 557698, 7, 6, 10, 10, 10, 9, 11, 4, 10, 10, 11, 12, 5, 74372260, 12, 8, 11, 12, 13, 6, 10, 9, 12, 12, 9, 7, 10, 8, 11, 9, 14, 12, 12, 8, 6, 11, 14, 11, 14, 12, 8, 5, 9, 158008465, 10, 8, 13, 15, 8, 5, 10, 4, 9, 10, 9, 8, 7, 9, 13, 8, 11, 10, 10, 10, 9, 13, 12, 10, 8, 6, 5, 10780097, 13, 5, 10, 11, 11, 13, 3, 7, 8, 7, 11, 7, 11, 10, 9, 10, 7, 10, 11, 7, 9, 6, 9, 12, 8, 12, 9, 10, 8, 6, 8, 12, 14, 6, 9, 14, 7, 5, 9, 10, 11, 11, 6, 6, 11, 7, 9, 12, 15, 11, 12, 12, 10, 9, 9, 13, 6, 15, 9, 12, 8, 5, 10, 7, 8, 14, 8, 11, 8, 10, 11, 5, 7, 7341503, 14, 11, 5, 495591, 8, 5, 13, 13, 13, 10, 8, 7, 10, 8, 13, 7, 11, 6, 6, 9, 9, 14, 11, 14, 8, 11, 6, 10, 8, 9, 13, 19530, 7, 14, 7, 9, 7, 11, 6, 9, 10, 6, 11, 8, 9434, 7, 14, 7, 7, 10, 11, 8, 11, 8, 12, 10, 11, 14, 402209815, 9, 12, 10, 6, 10, 7, 12, 8, 44419, 11, 11, 6, 12, 11, 7, 8, 12, 5, 4, 8, 9, 10, 10, 11, 7, 9, 5, 8, 6, 10, 14, 10, 9, 9, 5, 16, 6, 13, 11, 13, 10, 7, 7, 11, 13, 10, 13, 13, 10, 10, 14, 14, 9, 9, 6, 14, 5, 10, 7, 8, 13, 5, 6, 7, 6, 9, 11, 15, 15, 14, 9, 14, 12, 12, 13, 12, 6, 12, 9, 7, 4, 7, 16, 9, 8, 11, 16, 7, 123086, 8, 11, 10, 6, 10, 10, 1038617, 15, 9, 11, 14, 8, 16, 14, 10, 13, 8, 6, 12, 8, 8, 8, 11, 9, 9, 5, 6, 4, 11, 7, 14, 11, 5, 15, 7, 10, 12, 11, 9, 12, 10, 10, 15, 14, 8, 9, 8, 13, 13, 12, 10, 6, 8, 6, 6, 8, 13, 14, 10, 8, 11, 9, 13, 14, 13, 9, 13, 13, 11, 6, 11, 10}

Returns: {2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{5, 8, 10, 14, 11, 8, 11, 7, 9, 7, 11, 13, 9, 6, 5, 4, 7, 7, 8, 8, 8, 4, 11, 9, 8, 7, 7, 13, 12, 5, 6, 10, 8, 12, 6, 8, 11, 58009056, 9, 20594494, 4, 10, 9, 11, 7, 5, 9, 6, 10, 6, 13, 12, 11, 7, 6, 6, 5, 7, 9, 9, 10, 11, 8, 6, 10, 7, 10, 6, 13, 12, 9, 12, 7, 7, 9, 9, 8, 7, 9, 10, 15, 8, 11, 10, 9, 4, 11, 11, 8, 9, 8, 721593, 7, 11, 11, 9, 10, 10, 9, 6, 11, 8, 9, 14, 8, 10, 9, 9, 9, 9, 320777882, 10, 9, 14, 9, 7, 118061, 7, 7, 10, 9, 6, 13, 9, 3, 11, 11, 8, 10, 11, 13, 12, 8, 7, 8, 6, 8, 5, 8, 7, 10, 7, 13, 7, 14, 9, 9, 6, 12, 9, 4, 7, 7, 8, 8, 9, 5, 9, 6, 5, 9, 12, 6, 7, 6, 7, 6, 7, 7, 8, 11, 8, 8, 8, 6, 12, 13, 13, 7, 6, 13, 13, 6, 6, 9, 47885, 10, 9, 8, 11, 7, 11, 9, 8, 9, 7, 9, 14, 5, 11, 8, 8, 14, 9, 6, 13, 14, 13, 10, 14, 7, 9, 11, 7, 7585, 8, 13, 5, 9, 8, 5, 7, 8, 13, 6, 8, 6, 10, 8, 10, 9, 15, 12, 10, 14, 12, 11, 7, 13, 9, 7, 8, 12, 7, 9, 5, 6, 13, 11, 7, 9, 13, 6, 9, 6, 10, 9, 8, 12, 13, 9, 8, 7, 15, 5191728, 8, 13, 12, 11, 6, 3, 205265, 10, 5, 5, 11, 5, 4, 7, 10, 10, 12, 6, 12, 8, 7, 7, 9, 9, 5, 10, 13, 7, 5, 13, 12, 10, 10, 7, 9, 10, 4, 9, 9, 11, 7, 10, 6, 13, 9, 9, 10, 7, 7, 4, 12, 10, 10, 12, 13, 7, 5, 4, 10, 10, 9, 10, 7, 14, 8, 4, 11, 7, 7, 8, 9, 7, 7, 10, 10, 5, 8, 10, 8, 14, 11, 10, 9, 11, 11, 11, 5, 9, 6, 7, 8, 7, 10, 10, 13, 7, 8, 10, 9, 9, 9, 9, 7, 9, 8, 7, 5, 11, 10, 6, 10, 5, 11, 8, 12, 9, 6, 9, 10, 10, 6, 10, 8, 15, 10, 4, 8, 9, 8, 9, 10, 6, 8, 8, 8, 11, 3, 11, 10, 10, 8, 11, 7, 6, 5, 11, 8, 145462056, 11, 14, 7, 8, 12, 10, 6, 5, 13, 11, 8, 9, 8, 8, 12, 12, 9, 8, 12, 9, 4, 7, 8, 5, 10, 8, 11, 11, 12, 8, 13, 9, 7, 14, 7, 6, 12, 13, 6, 12, 4, 10, 8, 9, 7, 14, 10, 12, 12, 11, 10, 7, 4, 7, 15, 11, 57463214, 9, 6, 7, 5, 11, 7, 8, 8, 7, 6, 10, 9, 12, 9, 5, 8, 8, 8, 7, 10, 9, 5, 8, 14, 6, 9, 10, 27319, 9, 10, 9, 7, 5, 4, 11, 9, 5, 10, 5, 7, 10, 11, 7, 7, 8, 7, 8, 13, 5, 5, 12, 11, 9, 12, 11, 15, 10, 8, 11, 9, 13, 14, 8, 10, 14, 13, 8, 4, 8, 11, 11, 10, 5, 6, 7, 11, 14, 9, 8, 8, 13, 9, 8, 8, 9, 8, 10, 8, 7, 8, 8, 5, 12, 14, 9, 8, 4, 10, 8, 9, 6, 10, 12, 14, 9, 12, 7, 12, 9, 9, 12, 7, 9, 10, 11, 7, 8, 8, 4, 10, 11, 13, 6, 9, 10, 12, 14, 10, 2, 10, 10, 9, 8, 5, 7, 9, 326125, 11, 11, 10, 11, 12, 5, 6, 8, 6, 11, 9, 20198334, 14, 12, 6, 9, 14, 10, 12, 9, 4, 13, 9, 7, 10, 7, 6, 6, 7, 7, 10, 4, 12, 5, 10, 11, 10, 5, 13, 12, 7, 8, 10, 5, 9, 10, 9, 6, 11, 6, 6, 7, 9, 9, 8, 11, 8, 9, 11, 7, 7, 13, 10, 10, 10, 7, 13, 197461, 9, 12240, 8, 6, 5, 9, 4, 5, 9, 8, 5, 8, 464806691, 8, 12, 4, 7, 9, 8, 9, 8, 9, 10, 7, 10, 7, 8, 8, 13, 7, 8, 11, 4, 7, 12, 13, 13, 7, 13, 8, 11, 8, 5, 10, 10, 8, 8, 10, 9, 11, 10, 10, 9, 12, 11, 15, 11, 5, 6, 13, 14, 6, 8, 7, 10, 14, 6, 11, 9, 10, 9, 10, 12, 9, 14, 11, 9, 8, 8, 10, 7, 9, 10, 6, 12, 12, 13, 8, 7, 14, 4, 4, 12, 10, 8, 10, 9, 9, 8, 8, 12, 5, 6, 5, 5, 7, 6, 8, 7, 11, 8, 10, 12, 8, 7, 11, 6, 7, 8, 7, 11, 11, 9, 11, 8, 8, 7, 13, 14, 4, 430447, 10, 9, 11, 12, 6, 12, 7, 7, 5, 8, 13, 9, 10, 4, 6, 8, 14, 10, 7, 40486, 6, 9, 9, 10, 7, 8, 9, 8, 12, 12, 5084, 6, 7, 9, 10, 6, 10, 14, 5, 11, 8, 15, 6, 5, 6, 11, 6, 11, 7, 6, 12, 13, 10, 9, 13, 14, 9, 6, 12, 8, 8, 6, 10, 10, 11, 10, 7, 9, 13, 7, 10, 8, 9, 9, 13, 9, 9, 8, 9, 5, 13, 6, 6, 13, 12, 11, 7, 11, 10, 14, 13, 10, 7, 9, 10, 7, 6, 9, 7, 6, 7, 11, 11, 5, 9, 10, 7, 8, 9, 4, 11, 7, 9, 10, 10, 9, 12, 11, 7, 8, 15961, 14, 6, 6, 8, 9, 8, 9, 8, 8, 9, 5, 15, 8, 13, 13, 3397, 8, 12, 10, 14, 7, 7, 13, 9, 8, 8, 13, 6, 10, 8, 14, 8, 12, 9, 9, 11, 10, 10, 8, 6, 5, 10, 7, 8, 10, 7, 8, 10, 9, 12, 11, 11, 7, 13, 8, 14, 13, 9, 10, 10, 5, 6, 7, 10, 9, 13, 8, 8, 8, 9}

Returns: {-1 }
{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 }

Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258, 258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264, 265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271, 271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277, 278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284, 284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290, 291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297, 297, 298, 298, 299, 299, 300, 300, 301, 301, 302, 302, 303, 303, 304, 304, 305, 305, 306, 306, 307, 307, 308, 308, 309, 309, 310, 310, 311, 311, 312, 312, 313, 313, 314, 314, 315, 315, 316, 316, 317, 317, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 323, 323, 324, 324, 325, 325, 326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 341, 341, 342, 342, 343, 343, 344, 344, 345, 345, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 362, 362, 363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 372, 372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 401, 401, 402, 402, 403, 403, 404, 404, 405, 405, 406, 406, 407, 407, 408, 408, 409, 409, 410, 410, 411, 411, 412, 412, 413, 413, 414, 414, 415, 415, 416, 416, 417, 417, 418, 418, 419, 419, 420, 420, 421, 421, 422, 422, 423, 423, 424, 424, 425, 425, 426, 426, 427, 427, 428, 428, 429, 429, 430, 430, 431, 431, 432, 432, 433, 433, 434, 434, 435, 435, 436, 436, 437, 437, 438, 438, 439, 439, 440, 440, 441, 441, 442, 442, 443, 443, 444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 450, 451, 451, 452, 452, 453, 453, 454, 454, 455, 455, 456, 456, 457, 457, 458, 458, 459, 459, 460, 460, 461, 461, 462, 462, 463, 463, 464, 464, 465, 465, 466, 466, 467, 467, 468, 468, 469, 469, 470, 470, 471, 471, 472, 472, 473, 473, 474, 474, 475, 475, 476, 476, 477, 477, 478, 478, 479, 479, 480, 480, 481, 481, 482, 482, 483, 483, 484, 484, 485, 485, 486, 486, 487, 487, 488, 488, 489, 489, 490, 490, 491, 491, 492, 492, 493, 493, 494, 494, 495, 495, 496, 496, 496 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{3, 1, 2, 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258, 258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264, 265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271, 271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277, 278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284, 284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290, 291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297, 297, 298, 298, 299, 299, 300, 300, 301, 301, 302, 302, 303, 303, 304, 304, 305, 305, 306, 306, 307, 307, 308, 308, 309, 309, 310, 310, 311, 311, 312, 312, 313, 313, 314, 314, 315, 315, 316, 316, 317, 317, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 323, 323, 324, 324, 325, 325, 326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 341, 341, 342, 342, 343, 343, 344, 344, 345, 345, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 362, 362, 363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 372, 372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 401, 401, 402, 402, 403, 403, 404, 404, 405, 405, 406, 406, 407, 407, 408, 408, 409, 409, 410, 410, 411, 411, 412, 412, 413, 413, 414, 414, 415, 415, 416, 416, 417, 417, 418, 418, 419, 419, 420, 420, 421, 421, 422, 422, 423, 423, 424, 424, 425, 425, 426, 426, 427, 427, 428, 428, 429, 429, 430, 430, 431, 431, 432, 432, 433, 433, 434, 434, 435, 435, 436, 436, 437, 437, 438, 438, 439, 439, 440, 440, 441, 441, 442, 442, 443, 443, 444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 450, 451, 451, 452, 452, 453, 453, 454, 454, 455, 455, 456, 456, 457, 457, 458, 458, 459, 459, 460, 460, 461, 461, 462, 462, 463, 463, 464, 464, 465, 465, 466, 466, 467, 467, 468, 468, 469, 469, 470, 470, 471, 471, 472, 472, 473, 473, 474, 474, 475, 475, 476, 476, 477, 477, 478, 478, 479, 479, 480, 480, 481, 481, 482, 482, 483, 483, 484, 484, 485, 485, 486, 486, 487, 487, 488, 488, 489, 489, 490, 490, 491, 491, 492, 492, 493, 493, 494, 494, 495, 495, 496, 496, 497, 497, 498, 498, 499, 499, 499 }

Returns: {2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{159, 40, 292, 136, 167, 252, 440, 407, 363, 314, 265, 405, 25, 129, 107, 85, 154, 38, 325, 256, 72, 157, 231, 237, 123, 388, 155, 427, 9946, 245, 33, 135, 293, 120, 16, 254, 12, 344, 358, 111, 239, 328, 96, 299, 123, 396, 17, 233, 351, 144, 9928, 198, 318, 236, 244, 82, 152, 94, 37, 352, 413, 220, 230, 375, 2, 397, 247, 13, 136, 288, 9998, 91, 9971, 260, 411, 300, 8, 417, 444, 296, 347, 317, 114, 9942, 111, 447, 256, 437, 232, 345, 450, 62, 370, 9974, 89, 333, 295, 141, 9975, 80, 326, 9999, 161, 304, 214, 250, 311, 206, 215, 173, 253, 73, 335, 9917, 23, 424, 46, 188, 308, 402, 13, 138, 112, 377, 116, 57, 43, 287, 9990, 353, 190, 197, 18, 50, 9978, 219, 355, 9940, 358, 330, 14, 162, 53, 344, 67, 9941, 318, 9916, 421, 402, 423, 205, 385, 70, 227, 56, 182, 164, 145, 293, 178, 426, 156, 348, 194, 121, 99, 65, 9935, 143, 140, 196, 271, 290, 395, 44, 310, 163, 325, 282, 389, 253, 9991, 142, 42, 395, 362, 185, 52, 361, 173, 29, 438, 429, 306, 392, 436, 446, 280, 201, 302, 127, 7, 386, 48, 65, 162, 371, 12, 33, 337, 9995, 169, 338, 231, 9973, 257, 74, 380, 415, 302, 9965, 243, 60, 58, 305, 101, 182, 416, 78, 449, 381, 183, 222, 101, 2, 396, 425, 59, 86, 60, 81, 66, 70, 251, 440, 441, 363, 342, 252, 385, 9915, 158, 9996, 336, 9914, 225, 121, 376, 99, 366, 9911, 268, 18, 359, 147, 97, 159, 212, 330, 9947, 294, 9992, 34, 266, 45, 324, 61, 184, 305, 422, 9937, 153, 417, 160, 267, 9905, 408, 98, 414, 155, 103, 180, 263, 273, 42, 329, 72, 77, 9950, 9956, 349, 84, 62, 132, 408, 365, 9920, 242, 248, 41, 126, 327, 207, 262, 323, 31, 400, 200, 366, 110, 152, 443, 107, 297, 1, 403, 223, 244, 410, 122, 405, 5, 160, 211, 345, 95, 39, 110, 265, 394, 57, 128, 154, 54, 246, 44, 177, 299, 323, 84, 80, 274, 246, 179, 431, 215, 40, 9929, 9910, 134, 37, 112, 103, 174, 9968, 9953, 49, 115, 76, 9919, 90, 15, 240, 399, 126, 221, 134, 207, 9970, 9977, 281, 85, 298, 206, 181, 9930, 324, 421, 151, 55, 241, 386, 61, 347, 98, 350, 9934, 175, 21, 15, 146, 449, 43, 108, 404, 413, 9913, 315, 165, 423, 199, 179, 9986, 317, 83, 429, 49, 9924, 178, 93, 431, 166, 16, 76, 6, 286, 412, 17, 9904, 237, 217, 204, 309, 393, 420, 26, 89, 4, 276, 301, 139, 428, 261, 420, 35, 368, 191, 374, 114, 303, 146, 20, 170, 369, 87, 450, 92, 161, 275, 175, 202, 294, 130, 63, 30, 268, 9903, 289, 9, 259, 284, 71, 9939, 209, 9927, 9944, 196, 304, 9902, 342, 9952, 283, 348, 52, 401, 340, 9923, 235, 267, 445, 100, 75, 264, 409, 322, 364, 205, 144, 119, 411, 141, 9967, 8, 248, 401, 81, 106, 1, 332, 375, 236, 424, 92, 432, 276, 213, 210, 446, 220, 9, 266, 280, 9932, 218, 326, 409, 307, 164, 176, 199, 74, 168, 83, 88, 118, 22, 373, 367, 46, 258, 153, 71, 184, 301, 9984, 56, 249, 258, 38, 129, 281, 319, 36, 9951, 9922, 321, 279, 312, 4, 300, 444, 9926, 9989, 374, 333, 316, 188, 226, 53, 156, 158, 448, 380, 28, 384, 328, 443, 9943, 225, 319, 187, 27, 372, 9954, 260, 219, 93, 91, 68, 104, 313, 9906, 394, 172, 189, 312, 296, 210, 9981, 9933, 105, 238, 105, 232, 201, 364, 229, 157, 437, 148, 343, 3, 55, 186, 430, 349, 208, 127, 79, 148, 243, 439, 230, 337, 270, 438, 124, 64, 242, 255, 362, 425, 124, 412, 407, 343, 277, 41, 341, 382, 426, 191, 307, 391, 341, 216, 165, 30, 9957, 406, 279, 332, 125, 150, 262, 117, 208, 96, 190, 10, 383, 135, 320, 202, 357, 32, 34, 20, 261, 9938, 403, 354, 295, 31, 133, 272, 235, 130, 102, 422, 128, 9997, 9918, 125, 9948, 69, 59, 63, 339, 283, 439, 441, 327, 273, 9945, 255, 277, 181, 9988, 355, 138, 377, 9976, 187, 7, 357, 346, 214, 171, 320, 139, 415, 73, 383, 9931, 310, 86, 95, 272, 132, 239, 9961, 329, 428, 24, 315, 25, 198, 194, 338, 311, 51, 371, 288, 399, 131, 193, 66, 27, 448, 309, 241, 303, 9962, 192, 168, 9912, 104, 278, 216, 150, 335, 435, 172, 445, 137, 197, 419, 388, 270, 381, 79, 226, 88, 163, 297, 11, 169, 35, 442, 68, 264, 171, 183, 398, 390, 365, 379, 119, 275, 353, 9993, 78, 222, 387, 10000, 9959, 416, 360, 116, 189, 229, 339, 378, 11, 64, 269, 224, 356, 369, 113, 67, 384, 418, 9909, 147, 306, 368, 393, 316, 166, 346, 142, 352, 122, 167, 193, 174, 285, 48, 359, 291, 143, 410, 433, 382, 285, 435, 251, 321, 87, 274, 10, 29, 90, 257, 117, 450, 28, 19, 97, 233, 234, 94, 289, 278, 120, 419, 23, 224, 434, 108, 195, 192, 145, 271, 26, 334, 14, 314, 228, 390, 391, 69, 418, 238, 372, 331, 51, 100, 430, 234, 284, 115, 9921, 21, 282, 39, 9936, 9987, 291, 113, 9960, 9980, 433, 149, 223, 245, 47, 367, 336, 249, 36, 140, 203, 356, 351, 254, 9972, 9907, 109, 376, 9925, 250, 387, 240, 204, 378, 389, 406, 370, 109, 447, 82, 176, 106, 331, 442, 213, 47, 3, 436, 195, 432, 354, 217, 379, 313, 149, 9983, 308, 5, 186, 292, 151, 50, 298, 24, 221, 259, 287, 218, 203, 9949, 397, 434, 360, 404, 45, 133, 263, 211, 373, 77, 398, 75, 209, 22, 350, 6, 400, 322, 247, 286, 19, 9964, 427, 9958, 361, 9982, 131, 212, 32, 9994, 290, 227, 180, 185, 9969, 177, 340, 392, 334, 54, 102, 269, 9955, 228, 170, 9966, 9979, 9908, 9985, 414, 137, 58, 200, 9963, 118 }

Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

Returns: {0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 }

Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258, 258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264, 265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271, 271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277, 278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284, 284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290, 291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297, 297, 298, 298, 299, 299, 300, 300, 301, 301, 302, 302, 303, 303, 304, 304, 305, 305, 306, 306, 307, 307, 308, 308, 309, 309, 310, 310, 311, 311, 312, 312, 313, 313, 314, 314, 315, 315, 316, 316, 317, 317, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 323, 323, 324, 324, 325, 325, 326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 341, 341, 342, 342, 343, 343, 344, 344, 345, 345, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 362, 362, 363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 372, 372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 401, 401, 402, 402, 403, 403, 404, 404, 405, 405, 406, 406, 407, 407, 408, 408, 409, 409, 410, 410, 411, 411, 412, 412, 413, 413, 414, 414, 415, 415, 416, 416, 417, 417, 418, 418, 419, 419, 420, 420, 421, 421, 422, 422, 423, 423, 424, 424, 425, 425, 426, 426, 427, 427, 428, 428, 429, 429, 430, 430, 431, 431, 432, 432, 433, 433, 434, 434, 435, 435, 436, 436, 437, 437, 438, 438, 439, 439, 440, 440, 441, 441, 442, 442, 443, 443, 444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 450, 451, 451, 452, 452, 453, 453, 454, 454, 455, 455, 456, 456, 457, 457, 458, 458, 459, 459, 460, 460, 461, 461, 462, 462, 463, 463, 464, 464, 465, 465, 466, 466, 467, 467, 468, 468, 469, 469, 470, 470, 471, 471, 472, 472, 473, 473, 474, 474, 475, 475, 476, 476, 477, 477, 478, 478, 479, 479, 480, 480, 481, 481, 482, 482, 483, 483, 484, 484, 485, 485, 486, 486, 487, 487, 488, 488, 489, 489, 490, 490, 491, 491, 492, 492, 493, 493, 494, 494, 495, 495, 496, 496, 497, 497, 498, 498, 499, 499, 499 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
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Returns: {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3 }

Returns: {0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{6, 6, 6, 7, 9, 6, 9, 6, 7, 9, 11, 6, 6, 11, 6, 6, 11, 11, 6, 6, 8, 6, 6, 6, 6, 9, 6, 11, 6, 6, 9, 6, 7, 6, 6, 9, 6, 6, 9, 9, 9, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 7, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 7, 11, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 7, 7, 6, 6, 6, 6, 11, 6, 11, 6, 11, 6, 9, 6, 6, 11, 6, 11, 6, 9, 7, 9, 7, 7, 7, 6, 6, 11, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 9, 9, 6, 6, 11, 6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 11, 6, 11, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 9, 11, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 5198400, 6, 6, 6, 6, 6, 6, 6, 11, 9, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 9, 6, 6, 11, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 11, 6, 6, 6, 6, 6, 7, 6, 6, 6, 9, 6, 6, 11, 9, 7, 6, 11, 6, 6, 6, 6, 9, 6, 6, 6, 7, 11, 6, 6, 6, 9, 6, 11, 11, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 7, 6, 6, 6, 6, 11, 6, 9, 6, 7, 7, 6, 9, 6, 11, 11, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 9, 6, 7, 11, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 9, 11, 6, 11, 6, 6, 6, 6, 11, 11, 6, 6, 6, 7, 6, 6, 6, 6, 9, 6, 6, 9, 6, 6, 11, 6, 6, 9, 9, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 11, 6, 6, 6, 6, 6, 11, 11, 9, 7, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 9, 11, 6, 6, 6, 6, 11, 6, 6, 6, 6, 4864, 11, 6, 6, 6, 6, 11, 6, 6, 6, 7, 6, 6, 11, 9, 6, 6, 9, 6, 6, 9, 6, 6, 7, 6, 6, 11, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 7, 9, 6, 11, 11, 6, 6, 11, 9, 6, 6, 11, 7, 11, 6, 6, 6, 11, 6, 7, 6, 6, 6, 11, 6, 9, 6, 7, 6, 6, 6, 6, 9, 6, 11, 6, 6, 6, 9, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 11, 6, 6, 9, 6, 6, 11, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 11, 6, 6, 6, 6, 7, 11, 11, 9, 6, 6, 6, 9, 11, 6, 6, 9, 6, 6, 11, 11, 9, 6, 6, 6, 9, 9, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 9, 6, 6, 6, 7, 6, 7, 6, 9, 6, 6, 6, 6, 9, 11, 6, 6, 6, 11, 6, 9, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 11, 11, 9, 6, 9, 6, 6, 6, 11, 9, 11, 6, 6, 6, 11, 6, 6, 7, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 11, 6, 6, 6, 9, 11, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 11, 6, 9, 6, 6, 9, 6, 9, 6, 6, 6, 7, 7, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 9, 9, 6, 8, 11, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 9, 6, 6, 6, 11, 6, 6, 6, 6, 6, 9, 7, 6, 6, 11, 11, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 9, 11, 9, 6, 11, 9, 9, 6, 9, 6, 6, 6, 7, 11, 6, 6, 6, 6, 11, 7, 6, 6, 9, 6, 11, 9, 987654321, 6, 6, 6, 9, 9, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 9, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 7, 6, 11, 6, 7, 9, 6, 11, 6, 6, 7, 9, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 9, 11, 11, 6, 6, 9, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 6, 6, 11, 7, 6, 9, 11, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 11, 6, 6, 7, 6, 6, 6, 6, 6, 6, 11, 6, 6, 6, 6, 7, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 7, 6, 6, 11, 6, 6, 6, 7, 6, 11, 6, 6, 6, 7, 6, 6, 11, 6 }

Returns: {0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10 }

Returns: {-1 }
{1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3 }

Returns: {0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258, 258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264, 265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271, 271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277, 278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284, 284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290, 291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297, 297, 298, 298, 299, 299, 300, 300, 301, 301, 302, 302, 303, 303, 304, 304, 305, 305, 306, 306, 307, 307, 308, 308, 309, 309, 310, 310, 311, 311, 312, 312, 313, 313, 314, 314, 315, 315, 316, 316, 317, 317, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 323, 323, 324, 324, 325, 325, 326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 341, 341, 342, 342, 343, 343, 344, 344, 345, 345, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 362, 362, 363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 372, 372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 400 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3 }

Returns: {0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2 }
{1, 1, 5, 4, 5, 7, 4, 6, 8, 6, 6, 4, 5, 8, 9, 5, 5, 9, 8, 7, 8, 10, 10, 12, 10, 9, 9, 7, 9, 7, 10, 11, 9, 9, 7, 14, 12, 6, 6, 6, 7, 7, 7, 12, 11, 11, 9, 7, 5, 8, 6, 5, 6, 7, 7, 9, 8, 8, 8, 7, 10, 7, 5, 6, 6, 3, 5, 11, 8, 7, 7, 6, 6, 9, 8, 9, 11, 8, 8, 6, 7, 7, 7, 8, 8, 10, 10, 11, 11, 9, 9, 7, 7, 8, 4, 9, 7, 13, 11, 10, 7, 6, 6, 10, 10, 9, 7, 9, 9, 8, 10, 7, 5, 9, 8, 9, 11, 7, 6, 10, 8, 7, 9, 6, 9, 9, 8, 7, 6, 10, 10, 7, 7, 12, 13, 8, 9, 10, 12, 7, 10, 8, 11, 11, 11, 6, 7, 10, 8, 6, 11, 13, 12, 7, 8, 9, 6, 9, 10, 7, 8, 8, 7, 10, 9, 10, 8, 7, 8, 8, 9, 7, 8, 11, 10, 7, 7, 9, 8, 8, 7, 8, 7, 14, 12, 10, 10, 9, 9, 14, 12, 7, 8, 8, 8, 14, 12, 7, 8, 9, 9, 10, 10, 10, 10, 9, 9, 7, 8, 10, 12, 11, 11, 9, 9, 8, 8, 11, 11, 11, 12, 9, 8, 11, 11, 9, 8, 8, 9, 8, 9, 9, 9, 11, 11, 8, 8, 9, 9, 8, 8, 7, 8, 7, 7, 8, 9, 10, 9, 13, 13, 9, 9, 10, 9, 11, 10, 11, 11, 10, 10, 11, 11, 12, 11, 9, 9, 8, 8, 11, 10, 12, 12, 9, 8, 11, 10, 7, 8, 13, 12, 8, 10, 9, 9, 11, 9, 9, 10, 5, 5, 9, 11, 14, 13, 8, 9, 14, 16, 8, 8, 9, 9, 10, 9, 11, 11, 10, 10, 9, 8, 10, 10, 9, 10, 12, 12, 10, 10, 8, 7, 15, 15, 12, 12, 11, 10, 13, 13, 13, 13, 9, 9, 10, 11, 11, 12, 9, 8, 9, 10, 10, 10, 11, 11, 9, 9, 12, 13, 12, 12, 11, 10, 10, 10, 6, 5, 11, 10, 8, 8, 8, 8, 10, 10, 11, 11, 7, 7, 9, 9, 10, 10, 10, 10, 9, 10, 9, 10, 9, 9, 11, 11, 7, 6, 12, 12, 11, 10, 9, 9, 12, 12, 9, 9, 12, 14, 6, 7, 7, 7, 9, 9, 7, 8, 10, 9, 11, 11, 12, 11, 14, 13, 10, 10, 11, 11, 14, 12, 8, 8, 10, 10, 9, 10, 14, 14, 9, 9, 10, 8, 4, 4, 9, 9, 11, 13, 15, 13, 12, 10, 8, 8, 9, 10, 16, 14, 6, 7, 13, 14, 10, 11, 8, 8, 10, 9, 14, 13, 12, 10, 10, 9, 7, 8, 11, 11, 10, 10, 10, 9, 10, 10, 12, 11, 11, 10, 13, 13, 11, 10, 9, 9, 10, 11, 8, 8, 12, 10, 9, 9, 9, 9, 10, 10, 9, 9, 10, 10, 15, 14, 5, 7, 7, 7, 14, 14, 11, 10, 11, 11, 8, 8, 9, 9, 10, 10, 7, 7, 11, 10, 9, 9, 8, 8, 11, 11, 11, 9, 6, 6, 12, 11, 14, 15, 13, 13, 11, 11, 11, 11, 11, 11, 6, 6, 13, 13, 10, 10, 9, 9, 14, 14, 11, 11, 11, 14, 13, 13, 9, 9, 13, 14, 9, 9, 11, 10, 6, 5, 12, 13, 11, 12, 7, 7, 15, 14, 11, 11, 8, 8, 10, 9, 10, 11, 9, 9, 15, 15, 10, 11, 4, 4, 12, 11, 12, 12, 11, 10, 10, 10, 10, 9, 14, 15, 11, 11, 8, 8, 14, 14, 7, 7, 16, 14, 13, 13, 11, 12, 7, 7, 10, 11, 16, 15, 6, 6, 10, 10, 12, 12, 7, 7, 11, 12, 9, 10, 14, 14, 12, 12, 11, 11, 11, 12, 10, 10, 8, 8, 12, 12, 14, 14, 10, 10, 7, 7, 9, 8, 13, 13, 13, 13, 9, 9, 10, 10, 12, 11, 7, 7, 10, 10, 10, 10, 13, 14, 13, 12, 9, 10, 11, 11, 11, 11, 10, 11, 7, 6, 9, 9, 11, 12, 13, 13, 12, 12, 10, 10, 11, 12, 9, 9, 11, 10, 11, 11, 10, 10, 11, 12, 7, 8, 5, 5, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 7, 7, 9, 9, 11, 11, 12, 12, 15, 15, 12, 12, 14, 14, 9, 9, 10, 10, 9, 9, 13, 13, 9, 9, 8, 8, 6, 6, 13, 13, 9, 9, 10, 10, 9, 9, 12, 12, 15, 15, 10, 10, 8, 9, 10, 10, 7, 7, 10, 10, 15, 16, 12, 12, 10, 10, 9, 9, 13, 13, 7, 7, 11, 10, 14, 14, 11, 11, 10, 11, 10, 10, 12, 12, 12, 12, 12, 12, 11, 11, 9, 9, 11, 11, 10, 10, 13, 13, 11, 11, 11, 11, 10, 10, 12, 11, 9, 9, 12, 13, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 7, 7, 6, 6, 11, 11, 11, 11, 11, 12, 11, 11, 16, 16, 11, 11, 7, 6, 7, 7, 7, 7, 12, 12, 15, 15, 10, 11, 14, 13, 14, 14, 9, 9, 9, 9, 9, 8, 16, 16, 10, 10, 14, 13, 11, 11, 15, 15, 12, 12, 8, 8, 11, 11, 12, 12, 7, 7, 13, 13, 9, 9, 10, 10, 16, 16, 14, 14, 13, 14, 11, 11, 9, 9, 9, 9, 14, 14, 6, 6, 9, 9, 6, 6, 12, 12, 11, 11, 10, 10, 13, 13, 10, 10, 14, 14, 10, 10, 10, 10, 11, 11, 16, 16, 14, 14, 16, 17, 9, 9, 10, 10, 11, 11, 10, 10, 9, 9, 13, 13, 9, 9, 14, 14, 17, 17, 12, 12, 12, 12, 14, 14, 11, 11, 12, 12, 15, 14, 7, 7, 16, 15, 16, 16, 12, 12, 8, 8, 11, 11, 11, 11, 8, 8, 10, 10, 10, 10, 8, 8, 13, 13, 12, 12 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258, 258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264, 265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271, 271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277, 278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284, 284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290, 291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297, 297, 298, 298, 299, 299, 300, 300, 301, 301, 302, 302, 303, 303, 304, 304, 305, 305, 306, 306, 307, 307, 308, 308, 309, 309, 310, 310, 311, 311, 312, 312, 313, 313, 314, 314, 315, 315, 316, 316, 317, 317, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 323, 323, 324, 324, 325, 325, 326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 341, 341, 342, 342, 343, 343, 344, 344, 345, 345, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 362, 362, 363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 372, 372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 400 }

Returns: {1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 24 }

Returns: {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

Statistics

Problem Statement for "RedGreenBlueLight"

Problem Statement

Definition

Constraints

Examples