TopCoder Statistics - Problem Statement

Problem Statement

The Order of the Hats has commissioned the creation of a new hat rack. This new hat rack must meet certain properties in order to be considered to hold headwear of such importance. The hat rack is formed by taking several numbered knobs that are connected by rods. One of the knobs is nailed to the wall. The remaining knobs then hang below this top knob. A sample hat rack is shown in the picture below.

The picture also shows that the hat rack can be divided into levels of knobs. Formally, the level i is defined to contain each knob X such that there are exactly i rods between the top knob and knob X.

The order would like their hat rack to meet the following three requirements:

Each knob X can have at most two knobs hanging directly below it. If there is only one such knob, it hangs directly below X; otherwise, one knob will hang slightly to the right of X and the other slightly to the left.
Except for the bottommost level, each level must be full. That is, if level i is not the bottommost level, it must contain exactly 2^i knobs.
The bottommost level must have all its knobs as far on the left as possible.

The third requirement in more detail: Let b be the bottommost level. If we traverse level b-1 from left to right, there will first be some knobs with two rods going to knobs in level b, then possibly a single knob with one rod going to level b, and finally some knobs not connected to any knob in level b.

You are given a configuration of knobs and rods. The knobs are not fastened to the wall yet. The knobs are numbered 1 through N. There are precisely N-1 rods, and they are connecting the knobs in such a way that the entire structure holds together. (Thus, necessarily, the topology of the hat rack is a tree.)

You are given two int[]s knob1 and knob2, each containing N-1 elements. These two int[]s describe the rods: For each i, there is a rod connecting the two knobs knob1[i] and knob2[i]. Return the number of ways to arrange the hat rack such that it meets the requirements set by the Order of the Hats. Two arrangements are considered different if the relative position of at least one pair of knobs differs. If it is not possible to meet the requirements, return 0.

Definition

Class:: HatRack
Method:: countWays
Parameters:: int[], int[]
Returns:: long
Method signature:: long countWays(int[] knob1, int[] knob2)
(be sure your method is public)

Notes

The correct number of arrangements always fits in a signed 64 bit integer.

Constraints

knob1 will contain between 1 and 50 elements, inclusive.
knob1 and knob2 will contain the same number of elements.
Each element of knob1 will be between 1 and N, inclusive, where N is 1 + (the number of elements in knob1).
Each element of knob2 will be between 1 and N, inclusive, where N is 1 + (the number of elements in knob2).
Each pair of knobs in the hat rack will be connected by some sequence of rods and knobs.

Examples

{1}

{2}

Returns: 2
{1,1}

{2,3}

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

{2,3,4,5}

Returns: 0
{6,6,6,4,1}

{1,2,4,5,3}

Returns: 0
{1,1,2,2,11,11,8,8,3,3,4,4,5}

{2,3,11,8,12,13,9,10,4,5,7,6,14}

Returns: 16
{1,2,3,4,5,6,7,8,9}

{2,3,4,5,6,7,8,9,10}

Returns: 0
{2}

{1}

Returns: 2
{3, 1}

{2, 2}

Returns: 2
{2, 1, 3}

{4, 4, 2}

Returns: 2
{1, 5, 3, 2}

{4, 4, 1, 1}

Returns: 2
{1, 4, 2, 3, 5}

{5, 3, 5, 6, 6}

Returns: 2
{6, 2, 5, 1, 3, 7}

{5, 7, 4, 5, 7, 4}

Returns: 8
{8, 6, 5, 4, 7, 2, 1}

{1, 3, 6, 6, 5, 1, 3}

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

{7, 1, 5, 9, 5, 9, 1, 7}

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

{1, 1, 10, 7, 10, 4, 6, 4, 6}

Returns: 4
{11, 4, 8, 6, 7, 2, 1, 9, 10, 3}

{1, 11, 11, 9, 2, 5, 5, 1, 9, 2}

Returns: 16
{6, 9, 7, 8, 12, 4, 1, 10, 3, 2, 11}

{3, 1, 10, 3, 2, 5, 5, 4, 4, 1, 10}

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

{12, 13, 7, 13, 12, 5, 3, 6, 7, 3, 5, 6}

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

{8, 10, 1, 6, 6, 1, 10, 7, 8, 14, 11, 7, 14}

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

{3, 3, 2, 15, 10, 2, 9, 15, 1, 9, 1, 10, 5, 5}

Returns: 128
{6, 5, 3, 15, 10, 4, 1, 7, 11, 12, 8, 14, 2, 13, 9}

{8, 1, 16, 9, 16, 2, 3, 2, 7, 8, 10, 9, 10, 1, 3}

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

{17, 3, 10, 17, 10, 11, 6, 4, 3, 6, 2, 4, 12, 2, 11, 12}

Returns: 32
{3, 9, 12, 4, 1, 17, 18, 15, 6, 5, 11, 13, 14, 10, 7, 16, 2}

{5, 10, 8, 12, 16, 7, 7, 3, 16, 8, 14, 10, 4, 4, 12, 5, 3}

Returns: 32
{3, 11, 5, 6, 4, 9, 14, 16, 12, 15, 13, 2, 18, 7, 1, 8, 17, 19}

{18, 9, 1, 15, 3, 10, 3, 11, 17, 19, 15, 11, 19, 1, 9, 17, 18, 10}

Returns: 128
{11, 20, 15, 13, 12, 1, 18, 5, 3, 2, 7, 8, 16, 19, 14, 4, 17, 9, 6}

{9, 9, 2, 16, 4, 2, 5, 14, 4, 16, 13, 7, 10, 5, 10, 13, 1, 14, 7}

Returns: 64
{5, 1, 2, 11, 19, 12, 18, 17, 9, 4, 13, 15, 20, 7, 21, 14, 3, 10, 6, 8}

{16, 5, 10, 15, 13, 20, 11, 14, 13, 21, 20, 16, 5, 11, 15, 1, 21, 1, 10, 14}

Returns: 128
{20, 4, 11, 8, 1, 10, 21, 6, 2, 22, 16, 13, 9, 3, 18, 14, 15, 19, 7, 12, 5}

{19, 9, 17, 6, 2, 18, 20, 19, 5, 14, 20, 2, 3, 11, 5, 3, 18, 17, 14, 6, 11}

Returns: 128
{3, 12, 1, 7, 10, 11, 14, 19, 9, 6, 2, 23, 18, 20, 17, 8, 5, 16, 21, 15, 4, 13}

{20, 16, 6, 17, 8, 7, 22, 8, 16, 21, 6, 7, 14, 14, 5, 17, 22, 21, 5, 18, 20, 18}

Returns: 1024
{16, 2, 13, 21, 6, 11, 10, 9, 14, 3, 23, 1, 20, 15, 19, 17, 7, 18, 12, 24, 8, 4, 22}

{5, 15, 22, 23, 5, 2, 22, 12, 3, 6, 18, 3, 17, 16, 23, 18, 8, 16, 6, 17, 12, 2, 15}

Returns: 256
{14, 22, 25, 12, 11, 9, 2, 17, 4, 7, 8, 5, 15, 10, 24, 20, 1, 21, 18, 3, 13, 23, 16, 6}

{25, 12, 19, 19, 6, 12, 17, 14, 17, 23, 11, 11, 14, 9, 3, 22, 15, 15, 3, 6, 23, 22, 9, 25}

Returns: 512
{16, 18, 11, 10, 3, 25, 23, 20, 21, 14, 13, 6, 8, 19, 24, 12, 4, 5, 26, 7, 15, 9, 1, 22, 2}

{25, 11, 6, 12, 8, 17, 20, 16, 1, 17, 24, 25, 16, 24, 6, 14, 20, 11, 1, 8, 10, 14, 12, 9, 9}

Returns: 512
{7, 11, 3, 8, 1, 19, 17, 5, 10, 21, 13, 16, 6, 4, 24, 23, 12, 14, 15, 22, 9, 20, 2, 18, 26, 27}

{8, 23, 4, 25, 22, 2, 15, 4, 12, 12, 5, 2, 15, 26, 5, 7, 26, 3, 22, 8, 1, 23, 7, 1, 25, 3}

Returns: 2048
{21, 8, 24, 23, 7, 12, 6, 14, 11, 10, 16, 9, 1, 25, 15, 20, 28, 4, 22, 27, 3, 17, 19, 26, 2, 5, 13}

{14, 9, 26, 15, 11, 23, 22, 18, 15, 11, 4, 27, 4, 26, 27, 24, 3, 21, 9, 18, 21, 25, 3, 14, 24, 23, 25}

Returns: 1024
{23, 4, 22, 17, 9, 29, 2, 8, 14, 7, 18, 12, 21, 19, 1, 11, 26, 13, 3, 16, 20, 25, 28, 27, 5, 24, 10, 6}

{25, 26, 9, 28, 15, 28, 4, 27, 19, 3, 6, 15, 14, 12, 4, 6, 12, 3, 27, 25, 10, 22, 26, 9, 10, 14, 22, 19}

Returns: 2048
{16, 5, 17, 24, 4, 15, 29, 14, 18, 3, 21, 22, 25, 26, 8, 6, 9, 27, 13, 1, 10, 11, 12, 19, 28, 30, 20, 23, 2}

{6, 9, 8, 25, 19, 11, 8, 25, 27, 28, 1, 1, 7, 30, 22, 21, 24, 24, 30, 7, 19, 14, 11, 14, 21, 22, 9, 28, 6}

Returns: 2048
{24, 26, 12, 5, 29, 31, 15, 27, 11, 17, 22, 28, 14, 4, 25, 16, 10, 18, 1, 23, 6, 30, 13, 20, 9, 21, 7, 8, 2, 3}

{6, 12, 27, 19, 6, 29, 7, 5, 21, 21, 23, 8, 12, 30, 4, 24, 15, 24, 23, 27, 2, 5, 29, 15, 4, 7, 2, 30, 19, 8}

Returns: 32768
{19, 15, 1, 2, 22, 23, 21, 3, 27, 20, 24, 30, 14, 4, 29, 25, 6, 18, 28, 5, 17, 10, 8, 26, 32, 16, 31, 13, 9, 12, 7}

{20, 4, 5, 5, 29, 19, 15, 12, 1, 30, 32, 11, 28, 8, 4, 10, 32, 28, 16, 8, 10, 16, 11, 2, 20, 30, 2, 1, 19, 29, 15}

Returns: 2048
{19, 9, 26, 2, 11, 14, 17, 23, 18, 1, 20, 29, 13, 33, 24, 16, 22, 15, 27, 30, 28, 25, 8, 3, 21, 32, 7, 10, 6, 12, 5, 31}

{4, 32, 32, 30, 25, 21, 27, 15, 4, 25, 29, 14, 18, 14, 18, 28, 8, 13, 24, 24, 8, 21, 19, 28, 19, 13, 15, 27, 29, 22, 22, 30}

Returns: 4096
{3, 33, 15, 27, 5, 13, 2, 18, 11, 22, 12, 9, 29, 21, 34, 16, 23, 24, 31, 19, 10, 17, 6, 7, 28, 20, 14, 26, 32, 8, 25, 4, 30}

{18, 12, 26, 33, 6, 2, 5, 1, 12, 3, 18, 11, 33, 17, 31, 22, 27, 29, 32, 25, 27, 3, 1, 26, 2, 11, 25, 32, 6, 31, 5, 22, 17}

Returns: 4096
{3, 15, 33, 31, 14, 11, 5, 12, 7, 19, 6, 35, 26, 21, 34, 8, 24, 25, 16, 32, 2, 27, 10, 4, 20, 28, 22, 17, 13, 9, 23, 18, 29, 1}

{18, 1, 30, 4, 7, 9, 14, 18, 21, 33, 21, 32, 14, 30, 8, 33, 34, 17, 32, 27, 1, 19, 17, 7, 29, 29, 9, 8, 4, 19, 34, 6, 6, 27}

Returns: 16384
{13, 1, 24, 19, 36, 35, 9, 34, 8, 2, 11, 21, 23, 26, 28, 12, 33, 22, 32, 17, 5, 14, 27, 7, 15, 18, 20, 10, 4, 31, 29, 16, 6, 25, 30}

{6, 3, 13, 35, 6, 3, 16, 32, 2, 35, 14, 14, 36, 1, 2, 8, 28, 30, 30, 36, 13, 26, 25, 16, 31, 1, 31, 8, 28, 26, 25, 19, 18, 19, 18}

Returns: 8192
{29, 7, 19, 5, 20, 25, 1, 23, 12, 8, 21, 34, 9, 30, 33, 26, 11, 31, 37, 36, 24, 4, 10, 17, 22, 18, 13, 35, 16, 2, 15, 28, 27, 14, 3, 6}

{12, 27, 26, 17, 19, 30, 35, 22, 6, 3, 19, 1, 33, 12, 1, 15, 29, 33, 6, 27, 22, 2, 30, 37, 37, 8, 8, 15, 17, 3, 32, 29, 26, 2, 35, 32}

Returns: 16384
{23, 21, 9, 36, 30, 10, 16, 1, 2, 28, 14, 19, 37, 12, 13, 6, 15, 7, 4, 35, 33, 17, 34, 29, 8, 26, 5, 25, 31, 22, 27, 3, 38, 24, 32, 20, 11}

{24, 32, 22, 27, 9, 28, 38, 11, 10, 37, 6, 29, 18, 18, 9, 25, 28, 17, 32, 15, 10, 25, 11, 1, 17, 6, 24, 12, 38, 37, 34, 15, 22, 1, 34, 29, 12}

Returns: 16384
{11, 26, 31, 5, 29, 28, 22, 10, 1, 7, 18, 33, 14, 3, 2, 34, 30, 27, 16, 37, 24, 36, 8, 15, 39, 35, 13, 21, 20, 12, 38, 6, 32, 25, 17, 19, 23, 4}

{9, 28, 5, 14, 38, 9, 12, 4, 39, 4, 31, 2, 11, 8, 16, 2, 38, 21, 28, 21, 14, 19, 26, 8, 24, 19, 23, 24, 31, 26, 32, 23, 11, 12, 39, 5, 32, 16}

Returns: 131072
{37, 4, 28, 13, 3, 2, 16, 32, 19, 31, 33, 36, 35, 38, 39, 27, 12, 25, 5, 40, 11, 34, 24, 17, 8, 9, 30, 6, 20, 15, 26, 1, 14, 23, 29, 10, 18, 22, 7}

{1, 19, 29, 21, 35, 19, 18, 11, 15, 39, 14, 39, 13, 31, 21, 9, 31, 38, 29, 6, 15, 3, 34, 1, 33, 33, 38, 36, 11, 35, 12, 3, 13, 12, 36, 18, 14, 6, 34}

Returns: 32768
{8, 36, 18, 14, 34, 39, 12, 4, 28, 25, 11, 2, 10, 41, 15, 40, 31, 26, 17, 9, 21, 38, 29, 3, 16, 30, 19, 35, 1, 37, 7, 5, 23, 33, 24, 20, 13, 22, 6, 27}

{16, 19, 26, 18, 5, 8, 9, 36, 40, 11, 32, 6, 40, 14, 41, 25, 39, 32, 6, 11, 14, 29, 25, 19, 26, 39, 16, 7, 5, 7, 8, 18, 12, 12, 3, 36, 29, 3, 9, 41}

Returns: 65536
{15, 36, 42, 12, 30, 25, 31, 37, 14, 4, 26, 6, 5, 34, 3, 17, 11, 1, 40, 22, 2, 41, 28, 38, 19, 18, 8, 35, 32, 27, 33, 20, 10, 39, 9, 16, 29, 24, 23, 13, 21}

{21, 11, 29, 13, 40, 22, 35, 22, 4, 7, 41, 1, 6, 28, 10, 15, 40, 21, 15, 13, 30, 1, 14, 17, 12, 6, 26, 14, 38, 35, 28, 26, 41, 30, 12, 11, 17, 29, 38, 4, 7}

Returns: 65536
{1, 14, 42, 11, 21, 24, 3, 39, 32, 35, 9, 30, 18, 8, 34, 33, 5, 23, 12, 37, 31, 26, 7, 36, 15, 19, 10, 25, 16, 13, 27, 38, 22, 29, 43, 40, 2, 4, 6, 41, 17, 20}

{17, 7, 28, 26, 20, 20, 4, 42, 35, 12, 26, 35, 23, 21, 21, 23, 42, 5, 17, 13, 39, 37, 5, 1, 31, 22, 24, 29, 7, 6, 22, 1, 12, 37, 24, 4, 29, 39, 28, 31, 6, 13}

Returns: 262144
{44, 16, 42, 13, 27, 38, 10, 40, 41, 12, 8, 11, 34, 32, 7, 21, 3, 18, 23, 2, 1, 25, 6, 5, 30, 43, 24, 19, 17, 14, 31, 35, 9, 4, 33, 28, 29, 20, 22, 36, 15, 39, 26}

{19, 28, 43, 11, 19, 24, 18, 30, 37, 20, 4, 37, 16, 16, 43, 24, 25, 27, 14, 44, 4, 27, 44, 21, 39, 22, 13, 11, 20, 22, 38, 21, 18, 39, 38, 41, 14, 28, 13, 30, 2, 41, 25}

Returns: 131072
{40, 20, 16, 6, 37, 41, 15, 45, 13, 21, 18, 1, 17, 3, 34, 28, 36, 43, 35, 24, 12, 29, 19, 25, 9, 8, 30, 23, 11, 31, 10, 26, 42, 44, 7, 2, 4, 14, 32, 5, 39, 22, 27, 33}

{22, 13, 3, 28, 10, 8, 8, 24, 36, 4, 20, 26, 24, 27, 29, 39, 38, 31, 10, 14, 35, 13, 4, 31, 23, 39, 28, 38, 29, 14, 23, 37, 33, 33, 20, 26, 35, 9, 22, 3, 36, 37, 9, 27}

Returns: 262144
{30, 26, 1, 35, 17, 18, 33, 41, 20, 19, 25, 27, 15, 14, 13, 32, 16, 6, 8, 21, 46, 9, 4, 11, 22, 23, 29, 10, 24, 7, 38, 39, 36, 31, 45, 43, 42, 2, 34, 3, 44, 40, 5, 12, 28}

{45, 9, 24, 17, 22, 21, 31, 4, 37, 4, 15, 10, 45, 16, 30, 37, 24, 1, 33, 22, 32, 5, 10, 8, 20, 1, 15, 46, 31, 33, 30, 16, 27, 32, 20, 21, 7, 8, 27, 7, 9, 5, 46, 40, 17}

Returns: 262144
{35, 11, 47, 36, 4, 18, 43, 22, 2, 27, 14, 30, 12, 7, 41, 40, 45, 6, 25, 33, 5, 17, 29, 24, 37, 3, 19, 26, 39, 16, 44, 31, 46, 21, 13, 32, 23, 15, 38, 8, 28, 9, 20, 10, 42, 1}

{24, 10, 46, 17, 21, 34, 15, 18, 38, 46, 43, 29, 40, 21, 8, 5, 24, 36, 29, 13, 37, 22, 15, 2, 18, 8, 5, 27, 19, 22, 43, 19, 38, 17, 2, 27, 36, 37, 34, 16, 47, 10, 13, 16, 47, 40}

Returns: 4194304
{27, 39, 38, 20, 37, 1, 42, 5, 32, 25, 46, 43, 23, 15, 2, 24, 14, 7, 35, 36, 8, 31, 4, 13, 22, 26, 3, 34, 12, 6, 40, 17, 29, 30, 28, 18, 9, 11, 10, 45, 19, 16, 44, 48, 21, 41, 33}

{24, 11, 28, 43, 21, 3, 26, 42, 48, 39, 47, 46, 30, 20, 33, 3, 18, 37, 10, 17, 30, 28, 48, 24, 1, 41, 46, 10, 33, 20, 37, 29, 47, 11, 36, 21, 39, 41, 43, 1, 42, 6, 18, 26, 17, 29, 36}

Returns: 524288
{15, 45, 24, 32, 29, 30, 27, 25, 21, 8, 16, 22, 31, 13, 4, 41, 12, 36, 35, 3, 44, 14, 20, 17, 28, 2, 46, 40, 43, 10, 5, 39, 9, 1, 33, 19, 37, 42, 47, 26, 23, 18, 48, 6, 7, 38, 49, 11}

{32, 4, 10, 25, 42, 31, 30, 40, 16, 47, 17, 14, 34, 32, 31, 38, 47, 27, 34, 45, 16, 20, 18, 40, 46, 41, 38, 35, 1, 20, 11, 41, 14, 30, 19, 1, 10, 25, 4, 42, 11, 35, 45, 27, 46, 18, 19, 17}

Returns: 1048576
{21, 45, 9, 43, 37, 26, 46, 34, 39, 22, 29, 25, 48, 3, 40, 36, 13, 4, 16, 11, 7, 23, 32, 20, 2, 44, 33, 24, 12, 35, 19, 27, 1, 42, 47, 38, 31, 50, 30, 14, 5, 49, 8, 41, 6, 18, 10, 28, 17}

{1, 14, 11, 12, 25, 21, 12, 2, 46, 45, 45, 14, 35, 49, 15, 35, 38, 43, 46, 8, 40, 15, 23, 28, 8, 25, 28, 34, 32, 17, 10, 11, 42, 23, 50, 7, 38, 7, 50, 32, 10, 17, 40, 49, 21, 43, 1, 2, 42}

Returns: 1048576
{51, 49, 19, 25, 32, 9, 21, 31, 16, 34, 15, 14, 44, 43, 1, 48, 2, 35, 42, 12, 22, 29, 45, 4, 28, 3, 33, 24, 8, 50, 47, 7, 20, 6, 18, 39, 46, 38, 26, 40, 17, 5, 37, 27, 23, 13, 10, 41, 30, 11}

{20, 35, 23, 17, 36, 46, 7, 24, 8, 13, 3, 34, 23, 46, 51, 25, 35, 21, 30, 43, 38, 30, 8, 21, 9, 22, 48, 51, 22, 24, 34, 32, 17, 48, 9, 1, 38, 32, 3, 20, 36, 40, 4, 1, 25, 7, 4, 40, 13, 43}

Returns: 4194304
{5,7,1,5,2,8,6}

{8,8,4,3,5,4,4}

Returns: 0
{1,3,4}

{3,2,3}

Returns: 0
{7,5,5,7,4,5,6,2,2}

{3,2,3,8,1,1,1,10,9}

Returns: 0
{34, 46, 42, 29, 13, 51, 8, 30, 33, 49, 1, 26, 16, 44, 45, 26, 22, 6, 20, 18, 33, 2, 48, 31, 46, 18, 32, 5, 16, 13, 38, 27, 38, 1, 4, 26, 51, 25, 28, 46, 4, 29, 5, 23, 11, 3, 9, 22, 29, 29}

{7, 10, 12, 14, 15, 17, 19, 8, 21, 24, 30, 34, 35, 36, 37, 39, 40, 41, 6, 20, 42, 33, 2, 43, 31, 44, 18, 32, 45, 16, 13, 47, 27, 38, 1, 48, 26, 49, 25, 28, 46, 4, 50, 5, 23, 11, 3, 9, 22, 51}

Returns: 0
{40, 20, 2, 13, 14, 43, 44, 14, 51, 41, 12, 23, 3, 37, 47, 31, 18, 15, 18, 4, 45, 32, 40, 37, 7, 40, 31, 35, 38, 24, 2, 23, 26, 16, 26, 27, 19, 4, 32, 34, 18, 34, 6, 39, 33, 29, 19, 35, 46, 46}

{1, 5, 8, 9, 10, 11, 13, 17, 14, 20, 21, 12, 22, 3, 25, 28, 30, 36, 15, 41, 42, 43, 44, 45, 37, 7, 40, 31, 47, 38, 24, 2, 23, 48, 16, 26, 27, 49, 4, 32, 50, 18, 34, 6, 39, 33, 29, 19, 35, 51}

Returns: 0
{4, 9, 25, 43, 14, 20, 42, 32, 13, 34, 29, 22, 5, 16, 20, 9, 21, 17, 49, 26, 43, 29, 3, 36, 1, 17, 3, 43, 24, 21, 36, 39, 44, 44, 9, 17, 38, 17, 40, 14, 5, 25, 15, 19, 41, 48, 26, 47, 42, 42}

{2, 4, 6, 7, 8, 10, 11, 12, 18, 13, 23, 27, 22, 28, 16, 20, 30, 31, 32, 33, 34, 35, 29, 37, 45, 1, 46, 3, 43, 24, 21, 36, 39, 49, 44, 9, 50, 38, 17, 40, 14, 5, 25, 15, 19, 41, 48, 26, 47, 51}

Returns: 0
{35, 21, 16, 6, 42, 23, 22, 10, 30, 26, 51, 11, 29, 24, 30, 48, 51, 37, 10, 13, 7, 40, 18, 8, 17, 16, 21, 48, 10, 51, 10, 17, 46, 20, 4, 37, 16, 6, 13, 19, 28, 39, 26, 8, 45, 38, 22, 44, 5, 5}

{1, 2, 3, 9, 12, 14, 15, 23, 25, 27, 31, 32, 11, 29, 24, 30, 33, 34, 35, 36, 41, 7, 40, 18, 42, 43, 47, 21, 48, 49, 50, 10, 17, 46, 20, 4, 37, 16, 6, 13, 19, 28, 39, 26, 8, 45, 38, 22, 44, 51}

Returns: 0
{11, 5, 30, 9, 25, 13, 37, 18, 40, 13, 2, 3, 41, 4, 18, 12, 28, 17, 36, 8, 45, 50, 26, 3, 14, 38, 12, 34, 30, 31, 44, 51, 16, 31, 7, 40, 7, 36, 43, 19, 30, 44, 31, 34, 21, 48, 47, 1, 23, 23}

{6, 10, 5, 11, 9, 15, 20, 22, 24, 25, 13, 2, 27, 29, 4, 18, 32, 28, 17, 33, 8, 35, 37, 26, 3, 14, 38, 12, 39, 41, 42, 45, 46, 16, 49, 50, 40, 7, 36, 43, 19, 30, 44, 31, 34, 21, 48, 47, 1, 51}

Returns: 0
{28, 42, 22, 48, 21, 6, 19, 42, 49, 25, 27, 37, 51, 38, 29, 35, 32, 3, 26, 39, 20, 45, 40, 19, 10, 5, 48, 51, 16, 18, 47, 29, 11, 24, 4, 33, 28, 36, 47, 17, 41, 31, 34, 18, 27, 46, 32, 35, 50, 50}

{1, 2, 7, 8, 9, 12, 6, 13, 14, 15, 21, 22, 23, 25, 30, 37, 38, 42, 3, 26, 39, 20, 43, 40, 19, 10, 5, 44, 45, 16, 48, 49, 29, 11, 24, 4, 33, 28, 36, 47, 17, 41, 31, 34, 18, 27, 46, 32, 35, 51}

Returns: 0
{38, 40, 44, 34, 28, 49, 7, 9, 10, 25, 39, 47, 37, 24, 26, 2, 38, 10, 36, 48, 6, 2, 1, 39, 45, 21, 3, 43, 33, 8, 6, 21, 28, 35, 50, 36, 41, 29, 43, 42, 18, 41, 25, 6, 47, 46, 30, 24, 38, 38}

{4, 5, 11, 12, 13, 14, 15, 7, 9, 16, 17, 19, 20, 22, 23, 26, 27, 31, 10, 32, 34, 37, 2, 1, 39, 40, 44, 3, 45, 33, 8, 48, 21, 28, 35, 49, 36, 50, 29, 43, 42, 18, 41, 25, 6, 47, 46, 30, 24, 51}

Returns: 0
{21, 31, 21, 19, 13, 31, 2, 19, 49, 3, 19, 35, 35, 23, 29, 36, 5, 48, 36, 21, 24, 19, 40, 27, 28, 23, 21, 39, 12, 27, 27, 8, 37, 15, 46, 29, 24, 48, 30, 12, 22, 35, 24, 2, 1, 7, 26, 29, 3, 3}

{4, 6, 9, 10, 11, 13, 14, 16, 17, 18, 20, 25, 31, 32, 33, 34, 38, 5, 41, 36, 42, 43, 19, 40, 44, 28, 23, 21, 39, 45, 47, 27, 8, 37, 15, 46, 49, 50, 48, 30, 12, 22, 35, 24, 2, 1, 7, 26, 29, 51}

Returns: 0
{2, 24, 21, 33, 40, 49, 13, 19, 24, 22, 22, 30, 25, 36, 5, 15, 1, 40, 10, 39, 43, 25, 21, 9, 5, 50, 1, 8, 18, 15, 5, 14, 28, 10, 5, 21, 32, 24, 43, 36, 14, 46, 7, 32, 14, 16, 12, 44, 29, 29}

{3, 2, 4, 6, 11, 17, 20, 13, 19, 23, 26, 22, 27, 30, 31, 33, 34, 35, 37, 38, 39, 40, 25, 41, 9, 42, 45, 1, 8, 18, 15, 47, 48, 28, 10, 5, 21, 49, 24, 43, 36, 50, 46, 7, 32, 14, 16, 12, 44, 51}

Returns: 0
{6, 29, 7, 5, 28, 26, 12, 14, 48, 26, 26, 37, 44, 23, 1, 29, 26, 1, 51, 40, 49, 51, 46, 6, 5, 7, 27, 47, 51, 4, 1, 32, 22, 31, 36, 42, 50, 48, 9, 9, 25, 30, 12, 30, 11, 5, 12, 4, 41, 41}

{2, 3, 8, 10, 13, 15, 16, 17, 14, 18, 19, 20, 21, 24, 23, 28, 29, 26, 33, 34, 35, 37, 38, 39, 6, 40, 7, 27, 43, 44, 45, 1, 32, 22, 31, 36, 42, 46, 47, 48, 9, 25, 49, 50, 30, 11, 5, 12, 4, 51}

Returns: 0
{23, 12, 13, 43, 24, 36, 32, 22, 40, 50, 20, 23, 28, 5, 24, 29, 43, 1, 2, 35, 19, 5, 17, 13, 14, 4, 15, 38, 47, 42, 6, 36, 48, 30, 25, 11, 10, 46, 42, 15, 1, 21, 30, 22, 43, 1, 43, 45, 28, 28}

{3, 7, 8, 9, 12, 16, 18, 26, 27, 31, 32, 20, 23, 33, 34, 24, 29, 37, 39, 2, 35, 19, 5, 17, 13, 14, 4, 40, 38, 41, 44, 6, 36, 47, 48, 25, 11, 10, 46, 42, 15, 49, 21, 30, 22, 50, 1, 43, 45, 51}

Returns: 0
{39, 22, 20, 14, 45, 23, 33, 30, 7, 45, 47, 36, 13, 22, 47, 10, 18, 38, 34, 24, 8, 31, 6, 1, 36, 33, 4, 27, 26, 9, 37, 19, 26, 27, 18, 47, 41, 22, 39, 45, 9, 46, 7, 43, 23, 11, 15, 9, 12, 12}

{2, 3, 5, 16, 14, 17, 20, 21, 25, 28, 29, 30, 32, 13, 35, 40, 10, 42, 38, 34, 24, 8, 31, 6, 1, 36, 33, 4, 44, 48, 49, 37, 19, 26, 27, 18, 47, 41, 22, 39, 45, 50, 46, 7, 43, 23, 11, 15, 9, 51}

Returns: 0
{42, 27, 27, 12, 12, 43, 9, 43, 18, 18, 42, 34, 48, 51, 50, 49, 46, 5, 22, 10, 31, 13, 19, 51, 32, 47, 16, 42, 7, 2, 27, 1, 51, 17, 14, 19, 12, 22, 12, 7, 1, 44, 11, 30, 16, 7, 4, 12, 40, 40}

{3, 6, 8, 15, 20, 21, 23, 9, 24, 25, 18, 26, 28, 29, 33, 34, 35, 36, 5, 37, 10, 31, 13, 38, 39, 32, 41, 43, 42, 45, 2, 27, 46, 47, 17, 14, 19, 48, 22, 49, 50, 1, 44, 11, 30, 16, 7, 4, 12, 51}

Returns: 0
{30, 15, 31, 12, 32, 47, 9, 18, 10, 42, 31, 32, 18, 3, 29, 9, 25, 19, 47, 24, 38, 37, 18, 19, 44, 17, 17, 6, 13, 33, 28, 46, 21, 43, 48, 8, 32, 7, 46, 5, 3, 20, 28, 23, 8, 41, 7, 20, 13, 13}

{1, 2, 4, 11, 12, 14, 15, 16, 22, 10, 26, 27, 30, 31, 34, 29, 9, 25, 35, 36, 24, 38, 37, 18, 19, 39, 40, 17, 6, 42, 33, 44, 45, 21, 43, 47, 48, 32, 49, 46, 5, 3, 50, 28, 23, 8, 41, 7, 20, 51}

Returns: 0
{19, 14, 27, 35, 32, 22, 46, 24, 48, 10, 51, 32, 22, 4, 25, 27, 17, 6, 42, 6, 32, 13, 22, 30, 47, 32, 23, 9, 46, 42, 23, 47, 23, 1, 14, 25, 16, 11, 15, 11, 17, 7, 39, 12, 34, 51, 35, 49, 49, 49}

{2, 3, 5, 8, 18, 19, 20, 21, 24, 26, 10, 28, 29, 31, 4, 33, 27, 36, 37, 38, 6, 40, 13, 22, 30, 41, 32, 43, 9, 44, 42, 45, 46, 23, 1, 14, 25, 16, 47, 15, 11, 17, 7, 39, 12, 34, 48, 35, 50, 51}

Returns: 0
{38, 24, 46, 29, 31, 31, 49, 11, 8, 31, 10, 10, 15, 47, 13, 49, 16, 37, 21, 37, 27, 11, 42, 46, 25, 6, 42, 5, 51, 3, 46, 14, 11, 35, 5, 27, 16, 49, 47, 11, 12, 16, 34, 33, 44, 16, 13, 29, 31, 31}

{1, 2, 4, 7, 9, 17, 18, 19, 20, 8, 22, 23, 10, 15, 24, 26, 28, 30, 32, 21, 36, 37, 38, 39, 40, 25, 6, 41, 42, 43, 3, 45, 14, 46, 35, 5, 27, 48, 49, 47, 11, 12, 50, 34, 33, 44, 16, 13, 29, 51}

Returns: 0
{7, 26, 41, 24, 19, 9, 50, 48, 28, 50, 12, 40, 18, 3, 46, 48, 1, 27, 24, 31, 29, 17, 20, 12, 45, 22, 19, 32, 24, 51, 28, 22, 21, 40, 7, 50, 32, 33, 44, 39, 22, 28, 37, 51, 37, 13, 18, 47, 1, 51}

{2, 4, 5, 6, 8, 10, 9, 11, 14, 15, 16, 23, 25, 26, 3, 30, 34, 35, 27, 36, 31, 29, 17, 20, 12, 38, 41, 19, 42, 24, 43, 45, 46, 21, 40, 7, 48, 32, 33, 44, 39, 22, 28, 49, 50, 37, 13, 18, 47, 1}

Returns: 0
{24, 6, 44, 2, 7, 27, 35, 22, 42, 29, 3, 17, 48, 10, 33, 28, 28, 48, 35, 34, 27, 15, 13, 28, 21, 13, 18, 45, 10, 9, 24, 23, 33, 22, 50, 39, 24, 32, 15, 41, 44, 5, 35, 43, 16, 36, 43, 35, 1, 51}

{4, 8, 6, 11, 2, 7, 12, 14, 19, 20, 25, 3, 17, 26, 29, 30, 31, 37, 38, 40, 34, 27, 42, 46, 28, 21, 13, 18, 45, 10, 9, 47, 23, 33, 22, 48, 39, 24, 32, 15, 41, 44, 5, 49, 50, 16, 36, 43, 35, 1}

Returns: 0
{10, 47, 32, 42, 43, 23, 35, 11, 21, 50, 40, 29, 23, 16, 40, 23, 26, 51, 9, 1, 5, 22, 48, 50, 45, 8, 6, 44, 7, 46, 1, 7, 2, 1, 9, 17, 45, 6, 27, 38, 51, 2, 18, 19, 14, 42, 43, 23, 28, 28}

{3, 4, 10, 12, 13, 15, 20, 24, 11, 21, 25, 30, 29, 31, 16, 32, 33, 26, 34, 35, 36, 5, 22, 37, 39, 40, 8, 41, 44, 47, 46, 48, 7, 49, 1, 9, 17, 45, 6, 27, 38, 50, 2, 18, 19, 14, 42, 43, 23, 51}

Returns: 0
{12, 24, 33, 15, 29, 17, 32, 48, 20, 48, 39, 34, 3, 15, 38, 28, 48, 38, 41, 34, 48, 44, 11, 24, 34, 33, 26, 41, 26, 45, 4, 8, 11, 21, 21, 7, 11, 44, 22, 20, 10, 23, 41, 9, 44, 17, 46, 29, 51, 50}

{1, 2, 5, 6, 12, 13, 14, 16, 18, 19, 25, 27, 30, 3, 15, 31, 28, 32, 35, 36, 37, 38, 39, 40, 24, 34, 33, 42, 43, 26, 45, 4, 8, 47, 48, 21, 7, 11, 49, 22, 20, 10, 23, 41, 9, 44, 17, 46, 29, 51}

Returns: 0
{9, 1, 24, 7, 36, 21, 30, 23, 12, 6, 11, 37, 34, 2, 10, 26, 27, 14, 31, 38, 35, 22, 3, 13, 28, 4, 29, 17, 39, 8, 32, 25, 5, 33, 15, 16, 19, 18}

{20, 9, 9, 24, 20, 1, 7, 36, 24, 21, 20, 23, 7, 30, 36, 21, 26, 10, 30, 37, 31, 27, 34, 22, 27, 11, 3, 3, 6, 11, 6, 23, 34, 39, 28, 29, 5, 25}

Returns: 0
{33, 41, 46, 15, 2, 6, 11, 25, 35, 13, 37, 43, 38, 9, 5, 27, 29, 3, 45, 8, 32, 34, 24, 14, 16, 22, 23, 10, 26, 17, 12, 21, 18, 39, 4, 28, 31, 44, 40, 30, 20, 1, 19, 42, 36}

{7, 7, 33, 7, 33, 41, 46, 11, 11, 35, 6, 15, 13, 15, 41, 43, 13, 46, 25, 37, 5, 29, 27, 27, 8, 32, 32, 34, 10, 45, 26, 12, 24, 17, 45, 22, 29, 5, 39, 2, 12, 17, 31, 39, 37}

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

{3, 1, 2, 3, 3, 6, 15, 5, 8, 7, 16, 5, 8, 15, 4, 19, 16, 4}

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

{13, 13, 17, 21, 23, 21, 6, 17, 23, 12, 25, 22, 13, 6, 9, 3, 15, 25, 24, 9, 22, 19, 15, 16}

Returns: 0
{7, 5, 6, 8, 4, 11, 3, 10, 9, 2}

{1, 7, 5, 5, 1, 7, 4, 11, 8, 10}

Returns: 0
{32, 35, 37, 21, 24, 31, 1, 4, 8, 10, 5, 34, 6, 28, 20, 18, 33, 26, 11, 29, 19, 2, 27, 39, 22, 25, 16, 14, 23, 9, 38, 3, 36, 30, 17, 7, 12, 40, 13}

{15, 15, 35, 32, 15, 35, 21, 1, 31, 31, 4, 21, 34, 10, 8, 32, 8, 6, 10, 37, 18, 6, 24, 20, 24, 37, 11, 18, 16, 20, 14, 14, 2, 5, 29, 17, 38, 23, 9}

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

{3, 5, 3, 5, 2, 7, 3}

Returns: 0
{4, 5, 2, 1}

{3, 3, 5, 5}

Returns: 2
{8, 10, 26, 22, 17, 30, 3, 24, 32, 27, 20, 23, 25, 11, 7, 19, 15, 18, 2, 21, 28, 29, 9, 1, 5, 14, 6, 4, 12, 16, 13}

{31, 8, 31, 10, 31, 26, 30, 10, 22, 17, 8, 26, 27, 27, 30, 17, 19, 20, 15, 23, 32, 20, 11, 28, 21, 32, 23, 1, 24, 3, 24}

Returns: 0
{2, 3}

{1, 2}

Returns: 2
{17, 16, 9, 47, 32, 5, 7, 28, 46, 40, 3, 34, 14, 33, 26, 43, 1, 44, 25, 13, 15, 45, 23, 21, 19, 27, 29, 51, 22, 11, 10, 20, 4, 12, 18, 48, 49, 2, 31, 8, 50, 30, 42, 24, 38, 37, 36, 35, 39, 41}

{6, 17, 16, 16, 6, 9, 32, 17, 6, 28, 32, 28, 3, 47, 47, 14, 7, 33, 3, 1, 9, 33, 45, 23, 25, 13, 45, 26, 14, 34, 7, 11, 20, 51, 19, 23, 11, 44, 19, 18, 12, 51, 26, 42, 48, 44, 50, 37, 36, 2}

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

{14, 14, 14, 6, 19, 19, 17, 3, 17, 20, 18, 3, 8, 2, 7, 10, 8, 11, 13}

Returns: 0
{5, 4, 6, 7, 3, 1}

{2, 2, 4, 4, 5, 6}

Returns: 0
{31, 28, 4, 3, 26, 6, 21, 19, 23, 12, 17, 46, 45, 35, 1, 42, 30, 29, 13, 9, 5, 25, 34, 38, 43, 22, 7, 14, 39, 20, 40, 41, 36, 32, 24, 8, 18, 15, 37, 33, 16, 27, 2, 10, 44}

{11, 11, 11, 28, 28, 4, 3, 6, 31, 26, 31, 12, 12, 3, 21, 23, 17, 6, 45, 35, 42, 26, 23, 5, 46, 29, 34, 19, 4, 25, 29, 42, 25, 43, 19, 46, 7, 13, 1, 32, 37, 40, 20, 5, 40}

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

{10, 16, 16, 10, 10, 21, 9, 18, 15, 15, 9, 8, 1, 8, 23, 12, 22, 22, 12, 2, 19, 21}

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

{6, 6, 6, 3, 14, 12, 11, 11, 3, 17, 24, 7, 24, 8, 1, 7, 9, 20, 16, 10, 15, 17, 21}

Returns: 0
{3, 25, 12, 10, 27, 14, 24, 6, 16, 23, 19, 8, 4, 29, 7, 28, 11, 5, 17, 15, 22, 18, 21, 20, 9, 26, 2, 1}

{13, 3, 3, 12, 25, 10, 27, 24, 27, 12, 10, 25, 23, 14, 23, 8, 7, 29, 29, 5, 6, 14, 28, 8, 20, 15, 15, 4}

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

{10, 10, 3, 3, 10, 12, 9, 5, 12, 21, 21, 26, 13, 9, 26, 15, 1, 14, 24, 5, 19, 8, 6, 24, 20, 20}

Returns: 0
{8, 16, 22, 13, 28, 1, 19, 29, 24, 25, 31, 11, 32, 35, 6, 5, 15, 27, 34, 4, 14, 33, 20, 21, 30, 10, 3, 2, 18, 7, 23, 12, 17, 9}

{26, 26, 8, 8, 26, 28, 16, 22, 28, 29, 25, 31, 29, 19, 24, 32, 16, 6, 15, 32, 25, 1, 34, 4, 24, 14, 19, 15, 10, 27, 4, 7, 5, 6}

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

{14, 14, 14, 18, 12, 12, 13, 16, 2, 5, 17, 16, 9, 5, 3, 3, 13, 4}

Returns: 0
{18, 39, 44, 19, 8, 42, 43, 40, 15, 16, 49, 23, 12, 28, 38, 21, 29, 9, 36, 10, 27, 1, 6, 31, 35, 25, 17, 13, 11, 24, 41, 37, 34, 48, 47, 20, 45, 30, 26, 32, 7, 5, 4, 33, 14, 46, 2, 22}

{3, 3, 3, 39, 19, 8, 18, 44, 18, 8, 15, 39, 49, 49, 23, 15, 12, 40, 23, 29, 38, 19, 16, 12, 44, 16, 9, 21, 38, 1, 6, 25, 42, 24, 34, 21, 1, 47, 41, 42, 20, 9, 10, 11, 34, 48, 48, 13}

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

{10, 10, 10, 21, 16, 24, 21, 22, 5, 20, 11, 1, 22, 19, 12, 25, 19, 13, 2, 17, 1, 5, 11, 4}

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

{20, 20, 7, 20, 10, 19, 7, 23, 4, 13, 2, 25, 11, 23, 14, 19, 21, 4, 13, 9, 17, 10, 14, 9}

Returns: 0
{9, 6, 4, 7, 25, 10, 27, 13, 15, 3, 24, 29, 12, 23, 21, 19, 18, 8, 22, 2, 16, 1, 20, 28, 14, 5, 11, 26, 17}

{30, 30, 30, 6, 7, 25, 10, 25, 7, 4, 6, 15, 10, 4, 3, 9, 3, 27, 21, 8, 23, 16, 18, 16, 8, 23, 20, 9, 19}

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

{3, 15, 15, 3, 4, 8, 21, 8, 20, 3, 4, 22, 18, 21, 16, 18, 5, 6, 5, 9, 19}

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

{20, 20, 2, 6, 20, 7, 28, 2, 14, 14, 27, 28, 27, 7, 9, 4, 8, 13, 10, 8, 24, 1, 18, 5, 9, 12, 1}

Returns: 0
{9, 7, 11, 5, 6, 4, 1, 8, 10, 3}

{2, 9, 7, 11, 7, 9, 2, 6, 8, 10}

Returns: 0
{1}

{2}

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

{8, 5, 8, 1, 10, 5, 3, 10, 7}

Returns: 0
{10, 3, 7, 8, 4, 9, 1, 6, 11, 5}

{2, 2, 10, 3, 10, 8, 2, 8, 7, 3}

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

{12, 14, 14, 11, 18, 12, 11, 10, 18, 2, 5, 8, 3, 4, 2, 1, 9}

Returns: 0
{2, 1, 5, 3, 6}

{4, 4, 4, 2, 3}

Returns: 2
{15, 43, 3, 5, 8, 21, 27, 4, 29, 36, 41, 33, 17, 45, 47, 19, 32, 13, 25, 26, 39, 34, 6, 31, 38, 22, 44, 12, 46, 18, 30, 28, 14, 10, 40, 1, 11, 35, 16, 37, 20, 42, 24, 7, 23, 2}

{9, 15, 43, 3, 9, 15, 3, 43, 27, 27, 5, 36, 5, 33, 4, 8, 41, 8, 32, 13, 45, 47, 34, 26, 47, 38, 25, 21, 22, 12, 39, 18, 4, 41, 9, 33, 29, 31, 46, 35, 6, 31, 11, 38, 25, 16}

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

{9, 1, 9, 1, 7, 5, 5, 7}

Returns: 4
{9, 4, 8, 6, 18, 15, 1, 11, 17, 5, 13, 19, 7, 12, 16, 14, 3, 2}

{10, 9, 9, 10, 4, 4, 8, 8, 11, 18, 15, 6, 17, 1, 6, 10, 7, 12}

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

{1, 1, 6, 6, 10, 16, 10, 16, 8, 18, 15, 8, 1, 13, 5, 20, 7, 12, 15, 13, 7, 14, 5, 21}

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

{6, 13, 6, 13, 1, 11, 7, 9, 4, 9, 1, 10, 14, 4, 3}

Returns: 0
{3, 1, 2}

{4, 4, 1}

Returns: 2
{8, 29, 30, 3, 9, 20, 25, 17, 12, 6, 11, 7, 35, 33, 22, 34, 19, 4, 21, 18, 14, 27, 31, 32, 24, 1, 13, 23, 5, 10, 15, 16, 26, 28}

{2, 8, 8, 2, 3, 2, 20, 25, 30, 3, 25, 11, 6, 9, 17, 33, 29, 12, 4, 20, 19, 19, 17, 6, 33, 30, 31, 12, 22, 21, 22, 11, 10, 5}

Returns: 0
{11, 42, 2, 43, 21, 14, 32, 39, 25, 31, 34, 19, 8, 38, 9, 27, 6, 33, 26, 13, 37, 10, 36, 12, 1, 7, 23, 35, 41, 24, 18, 5, 29, 4, 16, 44, 17, 3, 22, 30, 28, 40, 20}

{15, 15, 15, 11, 11, 42, 21, 32, 39, 2, 31, 39, 21, 43, 42, 8, 9, 8, 14, 33, 31, 6, 25, 27, 26, 2, 38, 26, 43, 38, 6, 14, 25, 13, 9, 33, 18, 44, 35, 37, 18, 23, 10}

Returns: 0
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}

{51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51}

Returns: 0
{2, 4, 1}

{3, 2, 2}

Returns: 0
{3, 4, 1, 5}

{2, 2, 3, 4}

Returns: 0
{7, 4, 3, 6, 2, 5}

{1, 1, 7, 4, 4, 3}

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

{3, 3, 7, 7, 9, 9, 6, 8}

Returns: 0
{6, 5, 11, 7, 2, 3, 10, 9, 4, 8}

{1, 1, 6, 6, 5, 11, 11, 7, 7, 2}

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

{4, 4, 6, 6, 9, 9, 3, 3, 5, 1, 1, 2}

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

{7, 7, 2, 2, 8, 8, 14, 9, 9, 10, 10, 12, 12, 4}

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

{1, 1, 3, 3, 6, 6, 7, 7, 8, 14, 14, 13, 13, 16, 16}

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

{1, 1, 10, 10, 2, 2, 16, 16, 14, 14, 7, 7, 9, 5, 5, 11}

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

{6, 6, 18, 18, 2, 2, 3, 3, 8, 1, 1, 4, 4, 10, 10, 9, 9}

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

{12, 12, 2, 2, 8, 8, 18, 18, 1, 1, 16, 5, 5, 15, 15, 4, 4, 17}

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

{18, 18, 10, 10, 19, 19, 8, 8, 5, 5, 17, 17, 9, 16, 16, 2, 2, 11, 11}

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

{1, 1, 6, 6, 9, 9, 18, 18, 13, 13, 7, 7, 10, 10, 8, 8, 14, 15, 15, 21}

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

{7, 7, 8, 8, 19, 19, 14, 14, 5, 5, 22, 22, 11, 11, 24, 24, 9, 9, 23, 6, 6, 4, 4}

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

{11, 11, 25, 25, 21, 21, 14, 14, 17, 17, 5, 5, 4, 6, 6, 18, 18, 8, 8, 23, 23, 24, 24, 15}

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

{8, 8, 11, 11, 20, 20, 25, 25, 26, 26, 21, 21, 3, 2, 2, 5, 5, 23, 23, 7, 7, 10, 10, 13, 13}

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

{2, 2, 11, 11, 10, 10, 25, 25, 24, 24, 26, 26, 27, 27, 15, 15, 16, 16, 7, 6, 6, 12, 12, 9, 9, 5}

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

{14, 14, 3, 3, 24, 24, 15, 15, 21, 21, 12, 12, 18, 28, 28, 27, 27, 17, 17, 2, 2, 25, 25, 6, 6, 22, 22}

Returns: 0
{24, 7, 2, 18, 1, 15, 20, 29, 6, 9, 12, 23, 10, 16, 22, 4, 28, 25, 5, 3, 14, 13, 21, 17, 27, 11, 19, 26}

{8, 8, 24, 24, 7, 7, 2, 2, 18, 18, 1, 1, 15, 15, 20, 20, 29, 29, 6, 6, 9, 12, 12, 23, 23, 10, 10, 16}

Returns: 0
{25, 28, 31, 8, 11, 6, 12, 10, 13, 9, 3, 24, 26, 21, 16, 5, 1, 7, 30, 18, 29, 19, 27, 15, 22, 14, 4, 20, 2, 23}

{17, 17, 25, 25, 28, 28, 31, 31, 8, 8, 11, 11, 6, 6, 12, 12, 10, 10, 13, 13, 9, 9, 3, 3, 24, 24, 26, 26, 21, 16}

Returns: 0
{2, 28, 5, 27, 11, 18, 14, 22, 29, 7, 8, 20, 24, 23, 30, 25, 21, 4, 3, 12, 9, 19, 26, 6, 32, 17, 16, 10, 15, 31, 13}

{1, 1, 2, 2, 28, 28, 5, 5, 27, 27, 11, 11, 18, 18, 14, 14, 22, 22, 29, 29, 7, 7, 8, 20, 20, 24, 24, 23, 23, 30, 30}

Returns: 0
{27, 15, 21, 30, 3, 7, 23, 32, 9, 10, 5, 29, 1, 24, 25, 13, 16, 17, 6, 22, 2, 18, 14, 26, 12, 33, 31, 28, 11, 8, 19, 4}

{20, 20, 27, 27, 15, 15, 21, 21, 30, 30, 3, 3, 7, 7, 23, 23, 32, 32, 9, 9, 10, 10, 5, 5, 29, 29, 1, 1, 24, 24, 25, 13}

Returns: 0
{15, 2, 26, 12, 5, 9, 14, 13, 4, 11, 18, 6, 28, 21, 23, 30, 19, 22, 8, 34, 7, 29, 20, 1, 27, 3, 24, 33, 17, 16, 31, 32, 10}

{25, 25, 15, 15, 2, 2, 26, 26, 12, 12, 5, 5, 9, 9, 14, 14, 13, 13, 4, 11, 11, 18, 18, 6, 6, 28, 28, 21, 21, 23, 23, 30, 30}

Returns: 0
{25, 2, 23, 32, 13, 18, 19, 31, 34, 7, 20, 16, 27, 4, 17, 30, 12, 28, 11, 5, 8, 3, 35, 10, 15, 22, 6, 21, 9, 33, 24, 29, 26, 14}

{1, 1, 25, 25, 2, 2, 23, 23, 32, 32, 13, 13, 18, 18, 19, 19, 31, 31, 34, 34, 7, 20, 20, 16, 16, 27, 27, 4, 4, 17, 17, 30, 30, 12}

Returns: 0
{19, 4, 5, 14, 29, 27, 16, 30, 32, 15, 10, 8, 28, 23, 11, 13, 35, 12, 3, 21, 9, 34, 26, 18, 2, 24, 17, 31, 25, 6, 7, 1, 33, 20, 22}

{36, 36, 19, 19, 4, 4, 5, 5, 14, 14, 29, 29, 27, 27, 16, 16, 30, 30, 32, 32, 15, 15, 10, 10, 8, 8, 28, 23, 23, 11, 11, 13, 13, 35, 35}

Returns: 0
{11, 22, 34, 1, 7, 21, 36, 13, 5, 10, 30, 35, 37, 24, 14, 28, 27, 32, 29, 17, 6, 18, 26, 15, 25, 9, 3, 33, 2, 20, 16, 23, 12, 19, 4, 31}

{8, 8, 11, 11, 22, 22, 34, 34, 1, 1, 7, 7, 21, 21, 36, 36, 13, 13, 5, 10, 10, 30, 30, 35, 35, 37, 37, 24, 24, 14, 14, 28, 28, 27, 27, 32}

Returns: 0
{5, 12, 9, 17, 21, 4, 15, 11, 6, 3, 29, 37, 23, 27, 1, 20, 14, 2, 24, 36, 30, 32, 28, 13, 34, 8, 35, 31, 10, 19, 18, 33, 38, 16, 25, 7, 39, 26}

{22, 22, 5, 5, 12, 12, 9, 9, 17, 17, 21, 21, 4, 4, 15, 15, 11, 11, 6, 6, 3, 3, 29, 29, 37, 37, 23, 27, 27, 1, 1, 20, 20, 14, 14, 2, 2, 24}

Returns: 0
{2, 35, 28, 33, 16, 12, 29, 21, 32, 37, 6, 34, 39, 30, 22, 11, 8, 4, 23, 38, 13, 18, 25, 40, 1, 14, 36, 17, 26, 19, 5, 27, 31, 9, 20, 24, 15, 10, 7}

{3, 3, 2, 2, 35, 35, 28, 28, 33, 33, 16, 16, 12, 12, 29, 29, 21, 21, 32, 32, 37, 6, 6, 34, 34, 39, 39, 30, 30, 22, 22, 11, 11, 8, 8, 4, 4, 23, 23}

Returns: 0
{11, 12, 1, 8, 9, 27, 38, 24, 25, 31, 14, 29, 35, 7, 19, 28, 34, 10, 21, 30, 15, 36, 33, 32, 5, 39, 20, 3, 6, 22, 2, 18, 13, 23, 26, 16, 4, 41, 37, 40}

{17, 17, 11, 11, 12, 12, 1, 1, 8, 8, 9, 9, 27, 27, 38, 38, 24, 24, 25, 25, 31, 31, 14, 14, 29, 29, 35, 35, 7, 19, 19, 28, 28, 34, 34, 10, 10, 21, 21, 30}

Returns: 0
{6, 34, 33, 17, 4, 19, 40, 36, 29, 3, 14, 32, 15, 24, 10, 30, 22, 16, 35, 8, 42, 39, 28, 26, 2, 38, 9, 11, 5, 7, 37, 18, 41, 12, 27, 21, 1, 13, 31, 23, 20}

{25, 25, 6, 6, 34, 34, 33, 33, 17, 17, 4, 4, 19, 19, 40, 40, 36, 36, 29, 29, 3, 3, 14, 14, 32, 32, 15, 15, 24, 10, 10, 30, 30, 22, 22, 16, 16, 35, 35, 8, 8}

Returns: 0
{43, 1, 14, 27, 4, 35, 30, 10, 16, 36, 6, 20, 29, 5, 31, 15, 38, 12, 24, 33, 25, 22, 9, 3, 8, 19, 26, 34, 11, 40, 18, 28, 32, 13, 21, 7, 23, 41, 42, 17, 37, 39}

{2, 2, 43, 43, 1, 1, 14, 14, 27, 27, 4, 4, 35, 35, 30, 30, 10, 10, 16, 16, 36, 36, 6, 6, 20, 20, 29, 29, 5, 5, 31, 31, 15, 15, 38, 38, 12, 12, 24, 33, 33, 25}

Returns: 0
{20, 28, 24, 10, 17, 11, 34, 22, 12, 36, 38, 31, 29, 6, 42, 19, 2, 5, 40, 41, 13, 1, 37, 39, 23, 14, 9, 30, 15, 25, 16, 32, 4, 27, 3, 21, 33, 26, 35, 8, 44, 43, 7}

{18, 18, 20, 20, 28, 28, 24, 24, 10, 10, 17, 17, 11, 11, 34, 34, 22, 22, 12, 12, 36, 36, 38, 38, 31, 31, 29, 29, 6, 6, 42, 42, 19, 19, 2, 2, 5, 5, 40, 40, 41, 13, 13}

Returns: 0
{9, 42, 26, 6, 16, 44, 14, 18, 13, 8, 38, 30, 23, 15, 35, 10, 12, 29, 20, 40, 3, 43, 45, 25, 34, 28, 17, 7, 31, 27, 11, 33, 41, 21, 4, 22, 19, 24, 5, 39, 32, 1, 36, 2}

{37, 37, 9, 9, 42, 42, 26, 26, 6, 6, 16, 16, 44, 44, 14, 14, 18, 18, 13, 13, 8, 8, 38, 38, 30, 30, 23, 23, 15, 15, 35, 10, 10, 12, 12, 29, 29, 20, 20, 40, 40, 3, 3, 43}

Returns: 0
{20, 46, 15, 36, 25, 32, 45, 37, 22, 1, 8, 24, 19, 23, 11, 44, 17, 4, 9, 42, 41, 5, 12, 26, 43, 18, 34, 13, 39, 28, 30, 21, 7, 10, 27, 3, 14, 35, 29, 33, 40, 6, 16, 38, 31}

{2, 2, 20, 20, 46, 46, 15, 15, 36, 36, 25, 25, 32, 32, 45, 45, 37, 37, 22, 22, 1, 1, 8, 8, 24, 24, 19, 23, 23, 11, 11, 44, 44, 17, 17, 4, 4, 9, 9, 42, 42, 41, 41, 5, 5}

Returns: 0
{44, 8, 22, 29, 1, 18, 38, 36, 11, 33, 31, 7, 10, 15, 25, 39, 2, 21, 13, 6, 35, 43, 16, 14, 20, 45, 30, 23, 47, 5, 32, 42, 28, 4, 9, 34, 3, 46, 37, 40, 41, 24, 26, 17, 19, 12}

{27, 27, 44, 44, 8, 8, 22, 22, 29, 29, 1, 1, 18, 18, 38, 38, 36, 36, 11, 11, 33, 33, 31, 31, 7, 7, 10, 10, 15, 15, 25, 25, 39, 39, 2, 2, 21, 21, 13, 6, 6, 35, 35, 43, 43, 16}

Returns: 0
{46, 24, 15, 1, 20, 26, 31, 23, 37, 13, 7, 4, 16, 9, 8, 35, 38, 22, 2, 47, 41, 25, 3, 32, 44, 48, 10, 27, 42, 34, 29, 45, 11, 19, 21, 28, 12, 30, 14, 17, 33, 40, 39, 18, 36, 43, 5}

{6, 6, 46, 46, 24, 24, 15, 15, 1, 1, 20, 20, 26, 26, 31, 31, 23, 23, 37, 37, 13, 13, 7, 7, 4, 4, 16, 16, 9, 9, 8, 8, 35, 35, 38, 38, 22, 22, 2, 2, 47, 47, 41, 41, 25, 3, 3}

Returns: 0
{38, 39, 4, 32, 24, 37, 26, 1, 10, 19, 40, 14, 27, 20, 9, 18, 2, 46, 33, 23, 41, 6, 48, 31, 28, 12, 36, 45, 17, 22, 47, 13, 25, 29, 3, 15, 11, 5, 49, 43, 35, 34, 8, 30, 16, 7, 21, 44}

{42, 42, 38, 38, 39, 39, 4, 4, 32, 32, 24, 24, 37, 37, 26, 26, 1, 1, 10, 10, 19, 19, 40, 40, 14, 14, 27, 27, 20, 20, 9, 9, 18, 18, 2, 2, 46, 33, 33, 23, 23, 41, 41, 6, 6, 48, 48, 31}

Returns: 0
{8, 2, 3, 18, 17, 34, 6, 46, 14, 9, 49, 22, 28, 45, 12, 23, 25, 33, 20, 50, 37, 1, 47, 36, 42, 40, 32, 27, 38, 24, 31, 41, 30, 19, 16, 44, 5, 48, 21, 29, 7, 35, 39, 4, 11, 43, 15, 26, 10}

{13, 13, 8, 8, 2, 2, 3, 3, 18, 18, 17, 17, 34, 34, 6, 6, 46, 46, 14, 14, 9, 9, 49, 49, 22, 22, 28, 28, 45, 45, 12, 23, 23, 25, 25, 33, 33, 20, 20, 50, 50, 37, 37, 1, 1, 47, 47, 36, 36}

Returns: 0
{50, 23, 42, 31, 51, 47, 43, 39, 2, 48, 24, 41, 27, 16, 15, 11, 4, 28, 17, 32, 25, 45, 49, 37, 5, 44, 7, 8, 46, 12, 38, 9, 40, 30, 6, 22, 33, 35, 13, 21, 18, 26, 3, 14, 20, 1, 34, 19, 29, 36}

{10, 10, 50, 50, 23, 23, 42, 42, 31, 31, 51, 51, 47, 47, 43, 43, 39, 39, 2, 2, 48, 48, 24, 24, 41, 41, 27, 27, 16, 15, 15, 11, 11, 4, 4, 28, 28, 17, 17, 32, 32, 25, 25, 45, 45, 49, 49, 37, 37, 5}

Returns: 0
{3,2,2,1,7,1}

{2,5,6,4,5,3}

Returns: 0
{3,2,2,1,7,1,8,1}

{2,5,6,4,5,3,1,9}

Returns: 0
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 11, 11, 12 }

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

Returns: 0
{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 }

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

Returns: 1048576
{1, 1, 2, 2 }

{2, 3, 4, 5 }

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

{2, 3, 4, 5 }

Returns: 0
{1, 2, 3 }

{2, 3, 4 }

Returns: 2
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6 }

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

Returns: 8
{1, 1 }

{2, 3 }

Returns: 2
{1, 1, 2, 2, 3, 4, 4, 5, 5 }

{2, 3, 4, 5, 6, 7, 8, 9, 10 }

Returns: 0
{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 }

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

Returns: 4194304
{1, 1, 2, 2, 3, 3, 4, 4, 6, 6 }

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }

Returns: 0
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5 }

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }

Returns: 16
{1, 3 }

{2, 1 }

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

{2, 3, 4, 5 }

Returns: 0

Statistics

Problem Statement for "HatRack"

Problem Statement

Definition

Notes

Constraints

Examples