TopCoder Statistics - Problem Statement

Problem Statement

A Kingdom consists of several cities, some of which are connected by bidirectional roads. For any two cities A and B, there is exactly one simple path between them (a path is simple if it doesn't contain any city more than once). In terms of graph theory, the roads network in the Kingdom is a tree.

Unfortunately, the new King does not like trees, so he wants the road network to be a loop. In other words, each city must be directly connected to exactly 2 other cities, and for any two cities there still must be at least one path between them.

You will be given a String[] kingdom, representing the roads in the Kingdom. The i-th character in the j-th element of kingdom is equal to '1' (one) if there is a road between the i-th and the j-th cities, and '0' (zero) otherwise. Given that destroying a road or building a new road takes exactly one day, and knowing that King has only enough workers to perform 1 task per day, return the minimal number of days King needs to change the network to satisfy the new requirements. See examples for further clarification.

Definition

Class:: RoadsReorganization
Method:: minDaysCount
Parameters:: String[]
Returns:: int
Method signature:: int minDaysCount(String[] kingdom)
(be sure your method is public)

Constraints

kingdom will contain between 3 and 50 elements, inclusive.
Each element of kingdom will contain exactly n characters, where n is the number of elements in kingdom.
Each element of kingdom will contain only '0' (zero) and '1' (one) characters.
The j-th character in the i-th element of kingdom will be equal to the i-th character in the j-th element of kingdom.
The i-th character in the i-th element of kingdom will be '0'.
There will be exactly one simple path between every pair of cities.

Examples

{"010", "101", "010"}

Returns: 1

One day is needed to add the road between the 0-th and 2-nd cities.
{"0111", "1000", "1000", "1000"}

Returns: 3

Remove any single road, and add another two.
{"01010", "10100", "01000", "10001", "00010"}

Returns: 1

Add one road between the 2-nd and 4-th cities.
{"0100100", "1011000", "0100000", "0100000", "1000011", "0000100", "0000100"}

Returns: 5
{"011111", "100000", "100000", "100000", "100000", "100000"}

Returns: 7
{"010", "101", "010"}

Returns: 1
{"0011", "0010", "1100", "1000"}

Returns: 1
{"00010", "00010", "00011", "11100", "00100"}

Returns: 3
{"000110", "000011", "000001", "100000", "110000", "011000"}

Returns: 1
{"0100000", "1000001", "0001000", "0010101", "0001000", "0000001", "0101010"}

Returns: 3
{"00010000", "00101000", "01010000", "10100110", "01000000", "00010000", "00010001", "00000010"}

Returns: 5
{"000000010", "000001000", "000011011", "000000101", "001000000", "011000000", "000100000", "101000000", "001100000"}

Returns: 5
{"0000001000", "0001100010", "0000100001", "0100001000", "0110000000", "0000001000", "1001010000", "0000000010", "0100000100", "0010000000"}

Returns: 5
{"01011001010", "10000000000", "00000010000", "10000000000", "10000000000", "00000010000", "00100100001", "10000000000", "00000000001", "10000000001", "00000010110"}

Returns: 9
{"000010000100", "000000000100", "000000010000", "000000000100", "100000000000", "000000011000", "000000001010", "001001000101", "000001100000", "110100010000", "000000100000", "000000010000"}

Returns: 7
{"0000001000001", "0000000001010", "0000100000000", "0000100000000", "0011001000000", "0000001000000", "1000110100000", "0000001011100", "0000000100000", "0100000100000", "0000000100000", "0100000000000", "1000000000000"}

Returns: 7
{"00000000000100", "00000000000001", "00000001000000", "00000010000000", "00000000000100", "00000000000100", "00010000000100", "00100000001010", "00000000000001", "00000000000001", "00000001000100", "10001110001001", "00000001000000", "01000000110100"}

Returns: 13
{"010010100000001", "100000000000000", "000000000000001", "000000000001000", "100000010001110", "000000000001000", "100000000000000", "000010001100000", "000000010000000", "000000010000000", "000000000001000", "000111000010000", "000010000000000", "000010000000000", "101000000000000"}

Returns: 11
{"0000001000000000", "0000001110010000", "0000000010000000", "0000001000000000", "0000000000000001", "0000000000100010", "1101000000000000", "0100000000000000", "0110000000000110", "0000000000100000", "0000010001000000", "0100000000001000", "0000000000010000", "0000000010000000", "0000010010000001", "0000100000000010"}

Returns: 7
{"00000000000010100", "00000100000000000", "00000000000010000", "00000000000000100", "00000010000000000", "01000000000010000", "00001000000110000", "00000000100010000", "00000001000000000", "00000000000000010", "00000000000001000", "00000010000000000", "10100111000000010", "00000000001000100", "10010000000001000", "00000000010010001", "00000000000000010"}

Returns: 11
{"000000000001000010", "000000000010000100", "000000010100000000", "000000000000001000", "000000001000000000", "000000000000000100", "000000001000001100", "001000001000000001", "000010110001000000", "001000000000000000", "010000000000000000", "100000001000110000", "000000000001000000", "000000000001000000", "000100100000000000", "010001100000000000", "100000000000000000", "000000010000000000"}

Returns: 9
{"0000100010100000000", "0000000001010000000", "0000001000000000000", "0000000010000000000", "1000000000000000000", "0000001010000101100", "0010010100000000001", "0000001000000000000", "1001010000010010010", "0100000000000000000", "1000000000000000000", "0100000010000000000", "0000000000000000100", "0000010000000000000", "0000000010000000000", "0000010000000000000", "0000010000001000000", "0000000010000000000", "0000001000000000000"}

Returns: 15
{"00000010001000000000", "00000100000000000000", "00000100000000000000", "00000000010000000000", "00000100011000000000", "01101000000000000000", "10000000000000000000", "00000000000010001000", "00000000001000000000", "00011000000000000000", "10001000100011000001", "00000000000000000001", "00000001001000000000", "00000000001000000000", "00000000000000000010", "00000000000000000100", "00000001000000000010", "00000000000000010001", "00000000000000101000", "00000000001100000100"}

Returns: 11
{"000000000000000010001", "000000000100010000000", "000000001100100000010", "000000001000000000000", "000000000000000000001", "000000100010000000000", "000001000000000000000", "000000000000000010010", "001100000000000000000", "011000000010000100100", "000001000100000000000", "000000000000001010000", "001000000000000000000", "010000000000000000000", "000000000001000000000", "000000000100000000000", "100000010001000000000", "000000000000000000010", "000000000100000000000", "001000010000000001000", "100010000000000000000"}

Returns: 11
{"0000001000010000000000", "0000000000101000001000", "0001000000000000000001", "0010010000000000000000", "0000000000000010000000", "0001000000000011001100", "1000000000000000000000", "0000000010000000000010", "0000000100000000000000", "0000000000100000000000", "0100000001000000000000", "1000000000000000000100", "0100000000000000000000", "0000000000000000010000", "0000110000000000000010", "0000010000000000010000", "0000000000000000000001", "0000000000000101000000", "0100010000000000000000", "0000010000010000000000", "0000000100000010000000", "0010000000000000100000"}

Returns: 9
{"00000100000000000010000", "00001000000000000000001", "00000000100000000000000", "00000000001000101000000", "01000010000000000010100", "10000000000000000000000", "00001000100000100000000", "00000000000100000000000", "00100010000000010100010", "00000000000000100000000", "00010000000000000001000", "00000001000000100000000", "00000000000000100000000", "00000000000000010000000", "00010010010110000000000", "00000000100001000000000", "00010000000000000000000", "00000000100000000000000", "10001000000000000000000", "00000000001000000000000", "00001000000000000000000", "00000000100000000000000", "01000000000000000000000"}

Returns: 17
{"000101000001001000000000", "000100000000000000000000", "000000000000000000000100", "110010000100000001010100", "000100000000000000000000", "100000000000000000100000", "000000000001000000000000", "000000000000000000001000", "000000000000100000000000", "000100000000100000000010", "000000000001000000000000", "100000100010000000000000", "000000001100000000000000", "000000000000000000000100", "100000000000000000000000", "000000000000000000001000", "000000000000000000100000", "000100000000000000000000", "000001000000000010000000", "000100000000000000000000", "000000010000000100000100", "001100000000010000001001", "000000000100000000000000", "000000000000000000000100"}

Returns: 17
{"0000010100000010100000000", "0011000000000100000000001", "0100000000000000000000000", "0100001000000000000001000", "0000000010000000000000001", "1000000000010000000000000", "0001000000000000000000000", "1000000000000000000000000", "0000100000000000000000100", "0000000000000000000000001", "0000000000000000000010000", "0000010000000000000000000", "0000000000000001010000011", "0100000000000000000000000", "1000000000000000000100001", "0000000000001000000000000", "1000000000000000000000000", "0000000000001000000000000", "0000000000000000000100000", "0000000000000010001010000", "0000000000100000000100000", "0001000000000000000000000", "0000000010000000000000000", "0000000000001000000000000", "0100100001001010000000000"}

Returns: 17
{"00000100000000000000010000", "00000000000010000000000101", "00001000000000000000000000", "00000000010100000000000000", "00100000000000000000000010", "10000000001000000000000000", "00000000000000001000000000", "00000000000000000000000010", "00000000001000000000000000", "00010000001000000000000000", "00000100110000001000000010", "00010000000000000000000000", "01000000000000100000000000", "00000000000000000000000010", "00000000000010000000000000", "00000000000000001000000000", "00000010001000010000000000", "00000000000000000000000001", "00000000000000000000000010", "00000000000000000000000010", "00000000000000000000000010", "10000000000000000000001000", "00000000000000000000010000", "01000000000000000000000000", "00001001001001000011100001", "01000000000000000100000010"}

Returns: 19
{"000000000010000001100000000", "000000000000001000000000000", "000000000000000000001000000", "000000010000100000000000000", "000000000000000001000000000", "000000001000000000000000000", "000000000000000100000000000", "000100000000001000000000010", "000001000110000000000000000", "000000001000000000000000000", "100000001000010000000001010", "000000000000010000000000000", "000100000000000000000000000", "000000000011000000000010000", "010000010000000000000000000", "000000100000000000010000100", "000000000000000000000110000", "100010000000000000000000000", "100000000000000000000000000", "000000000000000100000000000", "001000000000000000000000100", "000000000000000010000000001", "000000000000010010000000100", "000000000010000000000000000", "000000000000000100001010000", "000000010010000000000000000", "000000000000000000000100000"}

Returns: 13
{"0000000000000000001000000000", "0000000000000000000100100000", "0000001000000010010000000000", "0000000000000010000000000000", "0000000000000000000001001010", "0000000000000010000000000000", "0010000000000000000000000000", "0000000000000000000001000000", "0000000000000000000000000001", "0000000000000100000001000000", "0000000000000000000100000000", "0000000000000000000000010001", "0000000000000000000010000000", "0000000001000001000000000000", "0011010000000000000001000000", "0000000000000100000000000000", "0000000000000000000000000110", "0010000000000000000000000000", "1000000000000000000000000001", "0100000000100000000000000000", "0000000000001000000000000100", "0000100101000010000000100000", "0100000000000000000001000001", "0000000000010000000000000000", "0000100000000000000000000000", "0000000000000000100010000000", "0000100000000000100000000000", "0000000010010000001000100000"}

Returns: 13
{"01000000010000010000000000000", "10000000000000000000000000000", "00010000101000000010000000000", "00100000000000000000000000010", "00000000000000000001000000000", "00000000000000000000000000001", "00000000000000000000010000000", "00000000000000000000000001000", "00100000000100010000000000000", "10000000000000000000000000000", "00100000000000000000000100100", "00000000100000000000000000000", "00000000000000010000000000000", "00000000000000010000000000000", "00000000000000000001100000000", "10000000100011000000000010000", "00000000000000000000000000010", "00000000000000000000000000010", "00100000000000000001001000000", "00001000000000100010000000000", "00000000000000100000000000000", "00000010000000000000001001000", "00000000000000000010010000000", "00000000001000000000000000000", "00000000000000010000000000000", "00000001000000000000010000000", "00000000001000000000000000000", "00010000000000001100000000001", "00000100000000000000000000010"}

Returns: 19
{"000000000000001000000000000000", "000000000000000000000000010000", "000000000000000000000000010000", "000000010000000000000000000000", "000000000000000001000000000000", "000000000000000000000100000000", "000000000010000000000000000100", "000100000000000000001001000000", "000000000000001100000000001000", "000000000000000000000010010000", "000000100000000000000000000000", "000000000000000000000000000100", "000000000000000000100000000000", "000000000000000001000000000000", "100000001000000000000101000000", "000000001000000000000000000000", "000000000000000000000000001000", "000010000000010000000000010000", "000000000000100000000000010000", "000000000000000000000000010000", "000000010000000000000000000000", "000001000000001000000000000000", "000000000100000000000000100000", "000000010000001000000000000100", "000000000000000000000010000000", "011000000100000001110000000101", "000000001000000010000000000010", "000000100001000000000001010000", "000000000000000000000000001000", "000000000000000000000000010000"}

Returns: 23
{"0000100010000000000000000000000", "0000010000000000000000000000100", "0000000000000000000001000000000", "0000000000010000000000000000000", "1000000000000000000000000000000", "0100000000000000000000000000000", "0000000010000000010100000000000", "0000000000000000000000001000000", "1000001000000000100000000000000", "0000000000100000000000000010001", "0000000001000011000000000001000", "0001000000000000000000000001000", "0000000000000001000010000100100", "0000000000000001000000100000000", "0000000000100000000000000000000", "0000000000101100000100001000000", "0000000010000000000000000000000", "0000001000000000000000000000000", "0000000000000000000000000000010", "0000001000000001000000010000010", "0000000000001000000000000000000", "0010000000000000000000010000000", "0000000000000100000000000000000", "0000000000000000000101000000000", "0000000100000001000000000000000", "0000000000001000000000000000000", "0000000001000000000000000000000", "0000000000110000000000000000000", "0100000000001000000000000000000", "0000000000000000001100000000000", "0000000001000000000000000000000"}

Returns: 15
{"00000000000000000100000000000000", "00000100000000000000000010000000", "00000010000100000000000000000000", "00000000000100000000000000000000", "00000000000000000000000000000010", "01000000000000000000000000000000", "00100001000000000000000000000000", "00000010000000001000000000000000", "00000000010010000100000000000000", "00000000100000000000010010000100", "00000000000001000000000000000000", "00110000000000000000000101000000", "00000000100001100000000000000000", "00000000001010000000000000000000", "00000000000010000000000000000000", "00000000000000000101000000100000", "00000001000000000000000000000000", "10000000100000010010000000010000", "00000000000000000100000001000001", "00000000000000010000000000000000", "00000000000000000000000010000000", "00000000010000000000000000000000", "00000000000000000000000000000001", "00000000000100000000000000000000", "01000000010000000000100000000000", "00000000000100000010000000000010", "00000000000000010000000000000000", "00000000000000000100000000001000", "00000000000000000000000000010000", "00000000010000000000000000000000", "00001000000000000000000001000000", "00000000000000000010001000000000"}

Returns: 17
{"000000000000000000001110000100100", "000000000000000000000001000000000", "000100000000100000000000000000000", "001000000000000000000000010000000", "000000000000000000000000000000010", "000000000000000000001000000000000", "000000000000000000001000000000000", "000000000100000000110100000000000", "000000000000000001001000000000000", "000000010000000000000000000000000", "000000000000100000000000000000001", "000000000000000000000100000000000", "001000000010000000000101100001000", "000000000000001000000000000000000", "000000000000010100000000000000000", "000000000000001000000000000100000", "000000000000000000000000100000000", "000000001000000000000000000000000", "000000010000000000000000000000000", "000000010000000000000000000000000", "100001101000000000000000000000000", "100000010001100000000000001000010", "100000000000000000000000000000000", "010000000000100000000000000010000", "000000000000100010000000000000000", "000100000000000000000000000000000", "000000000000000000000100000000000", "100000000000000100000000000000000", "000000000000000000000001000000000", "000000000000100000000000000000000", "100000000000000000000000000000000", "000010000000000000000100000000000", "000000000010000000000000000000000"}

Returns: 23
{"0000000000000000000000100000000000", "0000000000000010010000100000000100", "0000000000100000000100000000000000", "0000000000010000000100000000000000", "0000001000000000000000000000000000", "0000000000000000001000000010000000", "0000100100000000000010000001000000", "0000001010000000000000001000000000", "0000000100000000000000000000000000", "0000000000000000000001000000000000", "0010000000000000000000000000000000", "0001000000000000000000000000000000", "0000000000000000000000000010000000", "0000000000000000000100000000000000", "0100000000000000000000000000000000", "0000000000000000000000000100001000", "0000000000000000000000000010110000", "0100000000000000000000000000000000", "0000010000000000000000000000000000", "0011000000000100000010000000010000", "0000001000000000000100000000000000", "0000000001000000000000100000000000", "1100000000000000000001001000000000", "0000000000000000000000001000000000", "0000000100000000000000110000001001", "0000000000000001000000000000000000", "0000010000001000100000000000000000", "0000001000000000000000000000000000", "0000000000000000100000000000000010", "0000000000000000100100000000000000", "0000000000000001000000001000000000", "0100000000000000000000000000000000", "0000000000000000000000000000100000", "0000000000000000000000001000000000"}

Returns: 23
{"01000010000000000010001000000000000", "10010000000001000000000000010000001", "00000000000000000100000000000000000", "01000000000000000000000000000000000", "00000100000011000000000000000010000", "00001000000000000000000000000000000", "10000000000000000000000000000000100", "00000000000000000000000000000010000", "00000000000000000001000000000000000", "00000000000000000000100000000000000", "00000000000000010000000000000000000", "00000000000000100000100001000000000", "00001000000000000000000000000000000", "01001000000000000000000000000000000", "00000000000100000000000000000001000", "00000000001000000000000000010100000", "00000000000000000000100000000000000", "00100000000000000000100000000000010", "10000000000000000001000100100000000", "00000000100000000010000000000000000", "00000000010100001100001000000000000", "00000000000000000000000000010000000", "10000000000000000000100010000000000", "00000000000000000010000000000000000", "00000000000000000000001000000000000", "00000000000100000000000000000000000", "00000000000000000010000000000000000", "01000000000000010000010000000000000", "00000000000000000000000000000000001", "00000000000000010000000000000000000", "00001001000000000000000000000000000", "00000000000000100000000000000000000", "00000010000000000000000000000000000", "00000000000000000100000000000000000", "01000000000000000000000000001000000"}

Returns: 23
{"000100000000000000000000000000000000", "000000001000000000000000000000000000", "000000000000000000000000000001000000", "100000000000000000000000000000001000", "000000000000000100000000000000010000", "000000000000100000000000000000100000", "000000010000000000000000000000000010", "000000100000000000000000000000000000", "010000000000000000000000000100000001", "000000000001001000000000000000000000", "000000000000000000000000000000000010", "000000000100000000000001000000000000", "000001000000000000000010000001000100", "000000000000000100001100000000001000", "000000000100000000000100001000000000", "000010000000010000000000000000000100", "000000000000000000000000000000100000", "000000000000000000100000000000000000", "000000000000000001000000000000000010", "000000000000000000000000000000000010", "000000000000010000000000000000000000", "000000000000011000000000000000000000", "000000000000100000000000000000000000", "000000000001000000000000000000000000", "000000000000000000000000000000000100", "000000000000000000000000000011000000", "000000000000001000000000000000000000", "000000001000000000000000000000000000", "000000000000000000000000010000000000", "001000000000100000000000010000000000", "000001000000000010000000000000000000", "000010000000000000000000000000000000", "000100000000010000000000000000000000", "000000000000100100000000100000000011", "000000100010000000110000000000000100", "000000001000000000000000000000000100"}

Returns: 21
{"0000000000000000000000001011000000000", "0000001000000000000000000000000000000", "0000000001010000000000101000000000100", "0000010000000001001000000100000000001", "0000000000000000000000000010000000000", "0001000000000000000000000000000000000", "0100000000000000010000000000000000000", "0000000001000000000000000000000000000", "0000000000100000000000000000000001000", "0010000100000000000000000000000000000", "0000000010000000000000000000000000000", "0010000000000000010000000000000000000", "0000000000000000000000000000000000100", "0000000000000000000000000000000000001", "0000000000000000000000000000001000000", "0001000000000000000000000000000000000", "0000000000000000000000000100000000000", "0000001000010000000000000000000000000", "0001000000000000000000000000000000000", "0000000000000000000000000000000000100", "0000000000000000000001000000000000000", "0000000000000000000010000000000000010", "0010000000000000000000000000001000000", "0000000000000000000000000000100000000", "1010000000000000000000000000010000000", "0001000000000000100000000000000000000", "1000100000000000000000000000000000000", "1000000000000000000000000000000000000", "0000000000000000000000010000000000001", "0000000000000000000000001000000000001", "0000000000000010000000100000000100000", "0000000000000000000000000000001000000", "0000000000000000000000000000000000001", "0000000010000000000000000000000000010", "0010000000001000000100000000000000000", "0000000000000000000001000000000001001", "0001000000000100000000000000110010010"}

Returns: 23
{"00000000000000010000000000000000000000", "00000000000000000000000000000001000000", "00000010000001100000000000000000000000", "00000000000000000000000000000000010000", "00000000000000000001000000000000000000", "00000000000000001000000000000000000000", "00100000000000000010000000001000100000", "00000000000000000000000000000100000000", "00000000000000000100000000000010000000", "00000000000000000000000000000000001000", "00000000000000000000010000000000000000", "00000000000000000000000000000000000010", "00000000000000001000000000000000000000", "00100000000000000000000000000000000000", "00100000000000010000001000010001000000", "10000000000000100000000000000000011000", "00000100000010000000100000000000000000", "00000000100000000000000000000000000000", "00000010000000000000000000000000000000", "00001000000000000000001000000000000000", "00000000000000001000000000000000001000", "00000000001000000000000000000001000000", "00000000000000100001000000000000000000", "00000000000000000000000000010000000000", "00000000000000000000000000000000000010", "00000000000000000000000000100000000000", "00000000000000000000000001000000010010", "00000000000000100000000100000110000100", "00000010000000000000000000000000000000", "00000001000000000000000000010000000000", "00000000100000000000000000010000000000", "01000000000000100000010000000000000001", "00000010000000000000000000000000000000", "00010000000000010000000000100000000000", "00000000010000010000100000000000000000", "00000000000000000000000000010000000000", "00000000000100000000000010100000000000", "00000000000000000000000000000001000000"}

Returns: 25
{"000000000000000000000000000000100000000", "000000000000000000100000000000000000000", "000000000000000000000011010000000010001", "000000000000000000000000000000000000100", "000000000000000000010000000000010000000", "000000000000000000000000000000000000001", "000000000000000000101000000000010000000", "000000000000010000000000000000000000000", "000000000000000000000000000000000100000", "000000000000000000000000001000000000000", "000000000000000000001000000000000000000", "000000000000000100000000000000010000000", "000000000000000000000010000000000000000", "000000010000000001000000000000000000000", "000000000000000000000000001001000000000", "000000000001000000000000000000000000000", "000000000000000000000000001000000000000", "000000000000010000000000000010100100000", "010000100000000000000000000001001000000", "000010000000000000000000000000000000000", "000000100010000000000000000100000000000", "000000000000000000000000100001000000000", "001000000000100000000000000000001100000", "001000000000000000000000000000000000000", "000000000000000000000100000000000000000", "001000000000000000000000000000000000000", "000000000100001010000000000000000000000", "000000000000000000001000000000000000010", "000000000000000001000000000000000000000", "000000000000001000100100000000000000000", "100000000000000001000000000000000000000", "000010100001000000000000000000000000000", "000000000000000000100010000000000000100", "000000001000000001000010000000000001000", "001000000000000000000000000000000000000", "000000000000000000000000000000000100000", "000100000000000000000000000000001000000", "000000000000000000000000000100000000000", "001001000000000000000000000000000000000"}

Returns: 23
{"0000000010001000000000000000000000000000", "0000000000100000000000010001000001000000", "0000000000001000000000000000000000000000", "0000000000000100000000000000000000000000", "0000000000000000000000000000000000000010", "0000000000000000000000000100000000000000", "0000000000001000000000000000000000000000", "0000000000000000000000000000000000001000", "1000000000000000000000000000000000000000", "0000000000000000000000001100000000000000", "0100000000001001000001000000111000000000", "0000000000000000000000000000001000000000", "1010001000100000000000000000000000001000", "0001000000000010000000000000000000100000", "0000000000000100000010000000001110010001", "0000000000100000000000000000000000000000", "0000000000000000000000000000000000010000", "0000000000000000000000000000000000000100", "0000000000000000000000000100001000000010", "0000000000000000000000000000000001000000", "0000000000000010000000000000000000000000", "0000000000100000000000000000000000000000", "0000000000000000000000000000000100000000", "0100000000000000000000000000000000000000", "0000000001000000000000000000000000000000", "0000010001000000001000000000000000000100", "0000000000000000000000000000010000000000", "0100000000000000000000000000000000000000", "0000000000100000000000000000000000000000", "0000000000100000000000000010000000000000", "0000000000110010001000000000000000000000", "0000000000000010000000100000000000000000", "0000000000000010000000000000000000000000", "0100000000000000000100000000000000000000", "0000000000000100000000000000000000000000", "0000000000000010100000000000000000000000", "0000000100001000000000000000000000000000", "0000000000000000010000000100000000000000", "0000100000000000001000000000000000000000", "0000000000000010000000000000000000000000"}

Returns: 31
{"00000000000000000000000000000000000010000", "00000000000100000000000000000000000000000", "00000000001000000010100000000000000000000", "00000000000000100100001001000000001000100", "00000000000000000000001000000000000000010", "00000000000000000000100000000000000000000", "00000000000000000000000000000000100000000", "00000000000000000000000000000010000000000", "00000000001000000000000000100000000000000", "00000000000000000000000000000000000100000", "00100000100000000000000000000001000101000", "01000000000000000000000000000000000000010", "00000000000001000000000000000000000000000", "00000000000010000011000000000000000000000", "00010000000000000000000000000000000100000", "00000000000000000000000000000000000000100", "00000000000000000000000000000001000000000", "00010000000000000000000000000000000000000", "00100000000001000000000000000000000000000", "00000000000001000000000000000000000000000", "00100100000000000000010000000000000000000", "00000000000000000000100000000000000000000", "00011000000000000000000000000000000000000", "00000000000000000000000001000010000000000", "00000000000000000000000000000000000000001", "00010000000000000000000100000000000000000", "00000000100000000000000000000000000000000", "00000000000000000000000000000001000000000", "00000000000000000000000000000000010000000", "00000000000000000000000000000000011000000", "00000001000000000000000100000000000000000", "00000000001000001000000000010000000000000", "00000010000000000000000000000000001000000", "00000000000000000000000000001100000000000", "00010000000000000000000000000100100000000", "00000000011000100000000000000000000000000", "10000000000000000000000000000000000000100", "00000000001000000000000000000000000000000", "00010000000000010000000000000000000010001", "00001000000100000000000000000000000000000", "00000000000000000000000010000000000000100"}

Returns: 21
{"000000000000000000000000010000000000000000", "000000000000000000000000000000000000000001", "000000000000000001000001000000000000000000", "000000000000000000100000000000000000000000", "000000000100000000011010001000000000000000", "000000000000000000000000001000000000000000", "000000000000000000000000000000000000000100", "000000000000000001000000000000000000000000", "000000000100000000000000000000000000000000", "000010001000000000000000000000000000000100", "000000000000000001000000000000000000000000", "000000000000000000000000000000000000000100", "000000000000001001000000000000000000000000", "000000000000000000001000100000000000010000", "000000000000100000000000000000000000000000", "000000000000000000000000000000000000000001", "000000000000000000000000000000000000010000", "001000010010100000100000000000001000000001", "000100000000000001000000000000000000000000", "000010000000000000000000000000000000001000", "000010000000010000000100000000000000000000", "000000000000000000001000000000100000000000", "000010000000000000000001000000000100000000", "001000000000000000000010000000000001000000", "000000000000010000000000000000000000000000", "100000000000000000000000001000000000000000", "000011000000000000000000010001010010000000", "000000000000000000000000000000100000000000", "000000000000000000000000000000000000010000", "000000000000000000000000001000000000000000", "000000000000000000000100000100000000000000", "000000000000000000000000001000000000000000", "000000000000000001000000000000000000000000", "000000000000000000000010000000000000100000", "000000000000000000000000001000000000000000", "000000000000000000000001000000000000000000", "000000000000000000000000000000000100000000", "000000000000010010000000000010000000000010", "000000000000000000010000000000000000000000", "000000100101000000000000000000000000000000", "000000000000000000000000000000000000010000", "010000000000000101000000000000000000000000"}

Returns: 31
{"0000010000000000000000000000000000000000000", "0000000000000000000000000000000000000000010", "0000000100000000000000000000000000000000000", "0000000010000000000000000000000000000000000", "0000000100000000000000000000000000000000000", "1000000010000000000000000000100000000000000", "0000000000001000000000000000000000000000000", "0010100000000000010000010001010000000000000", "0001010000000000000000000000000000000000000", "0000000000000000000001000000000000000000000", "0000000000000000000000000000010000000000000", "0000000000000000000000000000100000000010000", "0000001000000000000000000000100000000000000", "0000000000000001000000000000000000000010000", "0000000000000000000000000010000001001000000", "0000000000000100000000001000000000000000000", "0000000000000000000001000100000000000000000", "0000000100000000000000000000000000000000000", "0000000000000000000000000000000100000000000", "0000000000000000000000000000000001000000000", "0000000000000000000000000000100000000000000", "0000000001000000100000000000000000001000000", "0000000000000000000000010000000000000000000", "0000000100000000000000100000000000000000011", "0000000000000001000000000000000000000000000", "0000000000000000100000000000000000000000000", "0000000000000010000000000000000000000000000", "0000000100000000000000000000000000000000000", "0000010000011000000010000000010001000000100", "0000000100100000000000000000101000000000000", "0000000000000000000000000000010000000000000", "0000000000000000001000000000000000001000000", "0000000000000000000000000000000000111000000", "0000000000000010000100000000100000000000000", "0000000000000000000000000000000010000000000", "0000000000000000000000000000000010000000000", "0000000000000010000001000000000110000000000", "0000000000000000000000000000000000000000100", "0000000000010100000000000000000000000001000", "0000000000000000000000000000000000000010000", "0000000000000000000000000000100000000100000", "0100000000000000000000010000000000000000000", "0000000000000000000000010000000000000000000"}

Returns: 29
{"00001000000000000000000100000000000000110000", "00000000000000000000000000000000000000001000", "00000000000000000000000000000000101000000000", "00000000000000000000100001000001000000000000", "10000000000000000000010000000000000000000000", "00000000000000000000000000000000000000000001", "00000000100000000000000000100000000000000000", "00000000001000000000000000000000000000000000", "00000010000000000000000000000000000000000000", "00000000000000000000000000000010000000000000", "00000001000000000001000000000000010000010100", "00000000000000000000000000000000000000001000", "00000000000000000000100000000000000000000000", "00000000000000000000000000000000001000000000", "00000000000000000000100000100010000001000000", "00000000000000000000000000001000000000010000", "00000000000000000000000000001000000000000000", "00000000000000000000000000000000000000000100", "00000000000000000000000000001000000000000000", "00000000001000000000000000000000000000000000", "00010000000010100000000000000000000000000000", "00001000000000000000000000000000000000000000", "00000000000000000000000000000100000000000000", "10000000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000", "00010000000000000000000000000000000000000000", "00000010000000100000000000000000000000000000", "00000000000000000000000000000000000000100000", "00000000000000011010000000000010000100000000", "00000000000000000000001000000000000100001000", "00000000010000100000000010001000100000000001", "00010000000000000000000000000000000000000000", "00100000000000000000000000000010000000000000", "00000000001000000000000000000000000000000000", "00100000000001000000000000000000000000000000", "00000000000000000000000000001100000000000000", "00000000000000000000000000000000000000010000", "00000000000000100000000000000000000000000000", "10000000000000000000000000010000000000000000", "10000000001000010000000000000000000010000000", "01000000000100000000000000000100000000000000", "00000000001000000100000000000000000000000000", "00000000000000000000000000000000000000000001", "00000100000000000000000000000010000000000010"}

Returns: 29
{"010000000001000000000000100000000000000001000", "100000000000000000010000000000001000001100000", "000000000000000000000000000000000000000001000", "000010000000000000000000000000000000000000000", "000100000000000000000000100000000000000000000", "000000000000000000000000000000000000000001000", "000000000000000000000000000100000000000000000", "000000000000000000000000000000000000000000010", "000000000000000000000000100000000000000000000", "000000000000000000000000000000100000000000000", "000000000000000000010000000000000000000000010", "100000000000000000000000000000000000010000000", "000000000000000000000000010000000000000000000", "000000000000000001000000000000000000000000000", "000000000000000100000110110000000000000000000", "000000000000001000000000000000000000000000100", "000000000000000000000000010000000000000000000", "000000000000010000100000100000000000000000000", "000000000000000001000000000000000000000000000", "010000000010000000000001000000000000000000000", "000000000000000000000000000010000000000000000", "000000000000001000000000000000000000000000000", "000000000000001000000000000000000000000000000", "000000000000000000010000000000000001000000001", "100010001000001001000000001000000000100000000", "000000000000101010000000000000000010000010000", "000000000000000000000000100000000000000000000", "000000100000000000000000000000010000000001000", "000000000000000000001000000000000001000000000", "000000000000000000000000000000000000010000000", "000000000100000000000000000000000000100000000", "000000000000000000000000000100000000000000000", "010000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000", "000000000000000000000000010000000100000000000", "000000000000000000000001000010000000000000000", "000000000000000000000000100000100000000000000", "000000000001000000000000000001000000000000000", "010000000000000000000000000000000000000000000", "010000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000", "101001000000000000000000000100000000000000000", "000000000000000100000000000000000000000000000", "000000010010000000000000000000000000000000000", "000000000000000000000001000000000000000000000"}

Returns: 31
{"0000000000000000000000000000000000000010000000", "0000000000000000000000000000000000000000000010", "0000100000000000000000001000000000000000010000", "0000000000000000100000000000000000000000000000", "0010000000000000100000000000000000000000000000", "0000000001000000000000000000000000000000000000", "0000000000000000000000001000000000001000000000", "0000000000000000000010100000000000010000000000", "0000000000010000000000000000000100000000000100", "0000010000000000000000000000000010000000000000", "0000000000000000000000000000000100000000000000", "0000000010000000000000000000000000000000000000", "0000000000000000000000000000000000100000000000", "0000000000000000000001000000000000000000000000", "0000000000000000000000001000010100000010101000", "0000000000000000001100010000000000000000000000", "0001100000000000000000000000000000000000000000", "0000000000000000000000000000000000000010000000", "0000000000000001000000000000000000000000000000", "0000000000000001000000000000000000000000000000", "0000000100000000000000000000000000000000000000", "0000000000000100000000000010000000000000000000", "0000000100000000000000001000000000000000000000", "0000000000000001000000000000000100000000000010", "0010001000000010000000100010000010000000000000", "0000000000000000000000000000000010000000000000", "0000000000000000000001001000000000000000000001", "0000000000000000000000000000000010000100000000", "0000000000000000000000000000000000000000100000", "0000000000000010000000000000000000000000000000", "0000000000000000000000000000000000010000000000", "0000000010100010000000010000000000000000000000", "0000000001000000000000001101000001000000000000", "0000000000000000000000000000000010100000000000", "0000000000001000000000000000000001000000000000", "0000000100000000000000000000001000000000000000", "0000001000000000000000000000000000000000000000", "0000000000000000000000000001000000000001000000", "1000000000000010010000000000000000000000000000", "0000000000000000000000000000000000000100000000", "0000000000000010000000000000100000000000000000", "0010000000000000000000000000000000000000000000", "0000000000000010000000000000000000000000000000", "0000000010000000000000000000000000000000000000", "0100000000000000000000010000000000000000000000", "0000000000000000000000000010000000000000000000"}

Returns: 25
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Returns: 33
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Returns: 27
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Returns: 29
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Returns: 31
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Returns: 23
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Returns: 63
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Returns: 21
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Returns: 27
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Returns: 27
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Returns: 21
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Returns: 21
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Returns: 23
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Returns: 19
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Returns: 73
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Returns: 79
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Returns: 67
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Returns: 23
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Returns: 69
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Returns: 17
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Returns: 29
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Returns: 73
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Returns: 57
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Returns: 29
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Returns: 81
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Returns: 23
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Returns: 17
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Returns: 27
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Returns: 27
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Returns: 65
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Returns: 25
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Returns: 23
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Returns: 25
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Returns: 25
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Returns: 21
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Returns: 17
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Returns: 27
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Returns: 53
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Returns: 63
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Returns: 21
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Returns: 19
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Returns: 21
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Returns: 47
{"00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000000010000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000001100000000000000100001000100000000001", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000000010000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000000010000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "01001100100110000111111110110001100110011011011010", "00000000000000000000000000000000000000100000000000", "10100011011000011000000001000000010001100100100100", "00000000000000000000000000000000000000001000000000", "00010000000000000000000000001010000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000010000000000000000000000000000000"}

Returns: 83
{"00000000000000000000000000000000000000000001001000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000000000000000000010000000000", "00000000010000000001000000000000000000000000001000", "00000000000000000000000000000000000000000000100000", "00000000001000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000100000000000000000", "00001000000000000000000000000000000000000000000000", "00000010000000000010000000000001000000000000000010", "00000000000000000000001000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000010000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000000001000000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000010000000000000000000000000", "00000000001000100000000000000000000010010000011000", "00001000000000000000000000000000000000000000000000", "00000000000000000000000000000100000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000100000000000000000000100001000000000000", "00000000000000000000000000000000100000000000000000", "00100000000000000100000000000000100000000000000000", "00000000000000000000000000100000000000000000000000", "00000000000000000000000001000000100000000000000000", "00000000000001000000000000001000000000000000000000", "00000000000000000000000000010000000000000000001000", "00000000000000000000100000000000100000100010000000", "00000000000000000000000000000000000000010000000000", "00000000001000000000000000000000000000000000000000", "00000000100000000000001110100100000000000100001100", "00000000000000000000000000000000000010000000000000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000000000000000100000", "00000000000000000010000000000000010000000000000001", "00000000000000000000001000000000000000000000000000", "00000000000000000000000000000100000000000000000000", "00010000000000000010000000000010000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000100000000000000000000", "10000000000000010000000000000000000000000000000000", "00000100000010000000010000000000000100001000001000", "00000000000000000010000000000000000000000000000000", "11001001000000001010000000001000101000000000100000", "00000000000000000000000000000000100000000000000000", "00000000001000000000000000000000000000000000000000", "00000000000000000000000000000000000010000000000000"}

Returns: 45
{"00000010000010000000000000000001000000000000000000", "00100000000000000000000000000000000000000000000000", "01000000000000000000000000000000000000000101000000", "00000000000000000000000000000000000010000000000000", "00000000000000000000000000000000000010000100001000", "00000000000000000001000000000000000000000000000000", "10000000000000000000000000000000000000000000000000", "00000000000000000000000000001000000000000000000001", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000100000000000000000000", "00000000000000000100000000000000000000000000000000", "00000000000000000001100000000000000000000000000000", "10000000000000000000000000000100010000000000000000", "00000000100000000000000000000100000000000000000000", "00000000000000000000000000000000000010000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000100000000000000000001000000000000", "00000000001000001000000000000001100000001000000000", "00000000000000000000000000000010010000000000000000", "00000100000100000000000010000000000000000000000000", "00000000000100000000000000000000000000000000000100", "00000000000000000000000000000000000100000000000100", "00000000000000000000000000010000000000000000000000", "00000000000000000000000000000000000001000000000000", "00000000000000010001000000000000000000000001000000", "00000000000000000000000000001000100000000000000000", "00000000000000000000000000000000001000000010000000", "00000000000000000000001000000000000100000000000000", "00000001000000000000000001000000000000000000000000", "00000000010011000000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "10000000000000000100000000000000000000100000000000", "00000000000000000100000001000000000000000000010000", "00000000000010000010000000000000000000000000000000", "00000000000000000000000000100000000000000000000010", "00000000000000000000010000010000000000000000000000", "00011000000000100000000000000000000000000000000000", "00000000000000001000000100000000000000000000000000", "00000000000000000000000000000001000000000000000010", "00000000000000000000000000000000000000001000000000", "00000000000000000100000000000000000000010000000000", "00101000000000000000000000000000000000000000000000", "00000000000000000000000000100000000000000000000000", "00100000000000000000000010000000000000000000000000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000100000000000001000", "00001000000000000000000000000000000000000000110000", "00000000000000000000110000000000000000000000000000", "00000000000000000000000000000000001000100000000000", "00000001000000000000000000000000000000000000000000"}

Returns: 19
{"00000000100000000000000100000000000000000000000100", "00000000000000000000000000000000000000001000000001", "00000000001000100000000000000000000000000000000000", "00000000000010000000000000000000000000000000000000", "00000000000000000000000000000000001000010010000000", "00000010000000000001000000000000000000000000000000", "00000100000010000000001000000000000000000000000000", "00000000000000000100000000000000000001000000000000", "10000000000000000000000000010000000000000000000000", "00000000000000000000000000000000000000000000100000", "00100000000100000000000000000000001000000000000000", "00000000001000000000000000000000000000000000000100", "00010010000000100000000000100000000000000000000000", "00000000000000001000000000001000000000000000010000", "00100000000010000000000000000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000001000000000000000000000100000000100000", "00000001000000000000100000010000000100000000000000", "00000000000000000000000011000100000000000000001000", "00000100000000000000000000000000000000000000000000", "00000000000000000100000000000000000000000000000000", "00000000000000000000001000000000000000000000000000", "00000010000000000000010000000000000000000000001000", "10000000000000000000000000000000000000000000000000", "00000000000000010010000000000000000010000001000000", "00000000000000000010000000000000000000000000000000", "00000000000010000000000000000001000000000000000000", "00000000100000000100000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000010000000000000000000000100000000", "00000000000000000000000000000001000000001000000000", "00000000000000000000000000100010000000000000000010", "00000000000000000000000000000000000100000000000000", "00000000000000000000000000000000000000000000001000", "00001000001000000000000000000000000000000000000000", "00000000000000001100000000000000100000000000000000", "00000000000000000000000010000000000000000000000000", "00000001000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000001", "00001000000000000000000000000000000000000000000000", "01000000000000000000000000000010000000000000000000", "00000000000000000000000000000100000000000000000000", "00001000000000000000000000000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000010000001000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000010001000000000010000000000000000", "10000000000100000000000000000000000000000000000000", "00000000000000000000000000000001000000000000000000", "01000000000000000000000000000000000000100000000000"}

Returns: 27
{"00000000000000100000000000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000100000000000000000000000000000", "00000000000000000000100000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000010000000000000000001000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000000001000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000100000000", "00000000000000100000000000000000000000000000000000", "00000000000000100000000000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "10000000000110000010000000010001000000000100000101", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000010000000", "00000000000000000000000000000000000000000100000000", "00000000000000100000000000000000000000000000000010", "00000000000000000000000000000000000000001000000000", "00110000000000000000000000000000110000000100000000", "00000100000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000001", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000100000000", "00000000000000100000000000000000000000000000000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000000000000001", "00000000000000000000000000000000000000000100000000", "00000000000000100000000000000000000000000000000000", "00000000000000000000100000000000000000000000000000", "00000000000000000000100000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000001000000100000100000000", "00000000000000000000000000000000000000000100000000", "00000111000000000001000100000000000010000100000000", "01001000011001110100100011100010001001111011010000", "00000000000000001000000000000000000000000100000000", "00000000100000000000000000000000000000000100101000", "00000000000000000000000000000000000000000001000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000001000000", "00000000000000100000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000000100000001000000100000000000000000000"}

Returns: 65
{"00000100100001000000000000000000000000000000000001", "00000000000010000000000000000000000000000000000000", "00000000000000000000000000000000000001000000000000", "00000000000000000110000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "10000000000000000000001000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000001000000000000100100000000000000000", "10000000000000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000010000000000000000000000", "00000000000000000000000001000000000000000000000000", "01000000000000010000000000000000000000000000000010", "10000000000000000000000000000000010000000000000000", "00000000000000000000000000000000100001000000000000", "00000000000010000000000000011010000001000000000001", "00000001000000000000000000000000000000000000000000", "00010000000000000000000000000000000000000000000000", "00011000000000000000000000000000000001000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000010000000000000000000", "00000000000000000000001000000000000000000000000000", "00000100000000000000010000000000000000000000000000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000000000011000000000", "00000000000100000000000000000000000010001000101000", "00000000000000000000000000000000000100000000000001", "00000000001000010000000000000000000000000000000000", "00000000000000010000000000000000000000000000000000", "00000001000000000000000000000000000000000000000000", "00000000010000010000100000000000000000000000000000", "00000000000000000000000000000000000000000000000010", "00000001000000100000000000000000000000000000000000", "00000000000001000000000000000000001000000010000000", "00000000000000000000000000000000010000000000000000", "00000000000000000000000000100000000000000000000000", "00000000000000000000000001000000000000000000000000", "00100000000000110010000000000000000000001000000000", "00000000000000000000000000000000000000000000000001", "00000000000000000000000010000000000000000000000000", "00000000000000000000000011000000000001000000000000", "00000000000000000000000000000000000000000000000110", "00000000000000000000000000000000010000000000000000", "00000000000000000000000000000000000000000000100000", "00000010000000000001000001000000000000000001010000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000101000000000000000000000000", "00000000000000000000000000000000000000000100000000", "00000000000010000000000000000001000000000100000000", "10000000000000010000000000100000000000100000000000"}

Returns: 33
{"00000000000001000000000000000000000000000000000001", "00000000100000000000000000000000000000000000000000", "00000100000000000000000001000000000000000000000000", "00000010000000000000000000010000000000000000000000", "00000000000000000000000000100000000001000000000000", "00100000000000000000000000000000000000001000000010", "00010000000000000000000000000000000000000000001000", "00000000000000000010000000000000000000000000000000", "01000000000000000000000000000010000000000000000000", "00000000000000000000010010100000000000000000000000", "00000000000000000000000010000000001000000000000000", "00000000000001000000000000000000010000000000000000", "00000000000000000000000000000000000000000101000000", "10000000000100000000000000000000000000100000010000", "00000000000000000000000000000000000000000000010000", "00000000000000000000100001000000000000000000000000", "00000000000000000000000000000010000000000000000100", "00000000000000000000000000000000000010000001000000", "00000001000000000000000100000000000000000000000000", "00000000000000000000000000000011000000000000000000", "00000000000000010000000000000100000000000000000000", "00000000010000000000000000000000000000000001000000", "00000000000000000000000000000000000000000100000000", "00000000000000000010000000010000000000000000000000", "00000000011000000000000000000000100000000000000000", "00100000000000010000000000000000000000010000000000", "00001000010000000000000000000000000000000000000000", "00010000000000000000000100000000000000000000000000", "00000000000000000000000000000000100100000000000000", "00000000000000000000100000000000100000000000100000", "00000000100000001001000000000000000000000000000000", "00000000000000000001000000000000000000000000000000", "00000000000000000000000010001100000000000000000000", "00000000000100000000000000000000000000000000000000", "00000000001000000000000000000000000000000000000000", "00000000000000000000000000001000000000000000000000", "00000000000000000100000000000000000000000010000000", "00001000000000000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000100000000000000000000000000000000000000000000", "00000000000010000000001000000000000000000000000000", "00000000000000000000000000000000000010000000001000", "00000000000010000100010000000000000000000000000000", "00000000000000000000000000000100000000000000000000", "00000000000001100000000000000000000000000000000000", "00000010000000000000000000000000000000000010000000", "00000000000000001000000000000000000000000000000011", "00000100000000000000000000000000000000000000000100", "10000000000000000000000000000000000000000000000100"}

Returns: 19
{"00000000000000000000000000000010000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000100000000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000001000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000010000000000000000000000000000000000000000", "00010100100001000000010000000110110011000001001000", "00000010000000000000000000000010000000000000000000", "00000000000000000000000100000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000010000000000000000000000000000000", "00001000000000000100100000000010000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00100000000100000000000000100010000000000010000001", "00000000000000000000000001000000000000000000000000", "00000000000000000001000010000010000000001000000000", "00000000000000000000000100000000000000000000000000", "00000000000000000000000000000000000001000000000000", "00000000000000000000000000000000100000000000000000", "00000000010000000000000000000000000000000000000000", "11000001011010111010000101000001001000110000110100", "00000000000000000000000000000010000000000000000000", "00000000010000000000000000001000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000010000000000000000000000000000000000000000", "00000000010000000000000000010000000000000100000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000000001000000000000", "00000000000000000000000100000000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000001000000010000100000000000010", "00000000000000000000000000000010000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000000000000010000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000100000000000000000000000000"}

Returns: 67
{"00000000000000000000000000000000000000000000000100", "00000100000000000000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000010000000000000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "01000000000000000100000000000000000000000100000000", "00000000001000000000010000000001001001000110000000", "00000000000000100000000000000000000000000000000000", "00000000000010000000000000000000000000000000000000", "00000000000000000000000000000000000000000001000000", "00000010000000000000000000000000000000000000000000", "00000000000000000000000000000000000100000000000100", "00010000100000100000000011000000000000011101000000", "00000000000000000000000000000000000000000000000100", "00000001000010000000100000000000010000000000000000", "00000000000000000000000000000000000000000000000100", "00000000000000000000000000000000000000000000000100", "00000100000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000100000000", "00000000000000100000000000000000000000000000000000", "00000010000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000001000000", "00000000000010000000000000000000000000000000000000", "00000000000010000000000000000000000000000000000000", "00000000000000000000000000000000000000000001000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000001000000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000001000000", "00000010000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000100", "00000000000000100000000000000000000000000000000000", "00000010000000000000000000000000000000000000000000", "00000000000100000000000000000000000000000000000000", "00000000000000000000000000000000000000000001000000", "00000010000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000100", "00000000000010000000000000000000000000000000000000", "00000000000010000000000000001000000000000000000000", "00001110000010000011001000010100000000000000010101", "00000010000000000000000000000000000000000000000000", "00000000010010000000000100100010000010000000100000", "00000000000000000000000000000000000000000001000000", "00000000000000000000000000000000000000000100000000", "00000000000000000000000000000000000000000000000100", "10000000000101011000000000000000100000100100001010", "00000000000000000000000000000000000000000000000100", "00000000000000000000000000000000000000000100000000"}

Returns: 65
{"00100000000000000000000000000000000000000000000000", "00000000001000000000000000000000001000001000000000", "10000000000000000000000000000000000000000010000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000001000000000000000010000001000", "00000000000000100000000000000000000001000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000001000000000000000000000000010000100000000", "00010000000000000000100000000010000000000000000000", "01000000100001000000000000000000000000000000000000", "00000000000000000000000000001000000000010000000000", "00000000000000001000000000000000100000000000000000", "00000010001000000000000000000100000100000000000000", "00000100000000000000000000010000000000000000000000", "00000000000000000000000100000000010000000000000000", "00000000000010000100000000000001000000000000000000", "00000000000000001001000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000000000100000000000000010000000000000000", "00000000010000000000000100000000000000001010000000", "00000000000000000000000010000000000000100000000000", "00001000000000000000000000000000000000000000000100", "00000000000000010000100000000000000000000000000000", "00000000000000000000010000100000000000000000000000", "00000000000000000000000000100000000000000000000100", "00000000000000000000000011000000000000000000000000", "00000000000000100000000000000000000000000000000000", "00000000000100000000000000000000000000000000100000", "00000000000001000000000000000000000000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000001000000000000000000000000000000000", "00000000000010000000000000000000000000000000000000", "00000000000000010001000000000000000000000000000000", "01000000000000000000000000000000000000000000000010", "00000000000001000000000000000000000000000000000001", "00000000100000000000000000000000000000000000000000", "00000100000000000000000000000000000000000000100000", "00000000000000000000010000000000000000000000010000", "00001000000100000000000000000000000000000000000000", "01000000000000000000100000000000000000000000000000", "00000000100000000000000000000000000000000000000000", "00100000000000000000100000000000000000000000000000", "00000000000000000000000000000000000000000000000001", "00000001000000000000000000001000000001000000000001", "00000000000000000010000000000000000000100000000000", "00001000000000000000000000000000000000000000000000", "00000000000000000000001001000000000000000000000000", "00000000000000000000000000000000001000000000000000", "00000000000000000000000000000000000100000001100000"}

Returns: 21
{"00000000000000000000000000000000000000000000000100", "00000000000100000000000000000100000000000000010000", "00000000000000000000000000000001000000000000000000", "00000000000000000000000000000000000000000000000100", "00000000000001000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000010000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "01000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000100", "00001100111000000011100011010011000100010100111111", "00000000000000000001000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000000100", "00000000000001000000010100000000000000000010000000", "00000000000001100000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000000000000100", "00000000000000000010000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "01000000000000000000000000000000000000000000000000", "00000001000001000000000000000000000000000000000000", "00100000000001000000000000000000110000000000000000", "00000000000000000000000000000001000000000000000000", "00000000000000000000000000000001000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000001000", "00000000000001000000000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000001000000000000000000000000000000000000", "00000000000000000010000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00000000000001000000000000000000000000000000000000", "01000010000001011000000000101000001011001001000000", "00000000000001000000000000000000000000100000000000", "10010000000011000100001000000000000000000000000000", "00000000000001000000000000000000000000000000000000", "00000000000001000000000000000000000000000000000000"}

Returns: 69
{"00000000000000000000000000000000000000000000100000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000100001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000010000000000000000000000000000000000000000", "00000000000000000000000000001000000000000000000000", "00000000000000000000000000000000100000001000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000001000000000000000000000000", "01000110111011111010000010000001110000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000100000000000000000", "00000000000000000000010000000000100000000000001000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000001000000000000000000000000", "00111001000100000101001001011100001101010000110110", "00000000000000000000000001000000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000100000000000000000", "00000000000000000000001000000000000000000000000000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000000000000000100000", "00000000000000000000000000000000000000000000100000", "10000000000000000000000100100010100010100111000001", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000001000000000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000000000000000100000"}

Returns: 79
{"00100000000000000001", "00000000000010000010", "10000100000000000000", "00000011000000000000", "00000000100000001000", "00100000100000000000", "00010000000100000000", "00010000000000010000", "00001100000000000000", "00000000000001100000", "00000000000000000001", "00000010000000000010", "01000000000000001000", "00000000010000010000", "00000000010000000100", "00000001000001000000", "00001000000010000000", "00000000000000100000", "01000000000100000000", "10000000001000000000"}

Returns: 1
{"00100000000000000000", "00100000000000000000", "11011111111111111111", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000", "00100000000000000000"}

Returns: 35
{"00000000100000000000000000100000000000000000000000", "00000000000000000010000000000000000000010000000000", "00000001000000000000000000000000000000000000000001", "00000000000000000000000001000000000001000000000000", "00000000010000001000000000000000000000000000000000", "00000000001000000000000000000000000000010000000000", "00000000000000100000000000000010000000000000000000", "00100000000000000000000000000001000000000000000000", "10000000000000000000000100000000000000000000000000", "00001000000000000000000000000000100000000000000000", "00000100000000000001000000000000000000000000000000", "00000000000000000000001000000000000000100000000000", "00000000000000000000000000000000000100000000000000", "00000000000000000000000000000000010000000000010000", "00000010000000000000000000000000000000000100000000", "00000000000000000000001000000100000000000000000000", "00001000000000000000000000000000001000000000000000", "00000000000000000000000000000000000000000011000000", "01000000000000000000000000000000000000100000000000", "00000000001000000000000000000000000000000000000000", "00000000000000000000010000100000000000000000000000", "00000000000000000000100000000000000100000000000000", "00000000000100010000000000000000000000000000000000", "00000000100000000000000000000000000010000000000000", "00000000000000000000000000000000000000000100001000", "00010000000000000000000000000000000000000000000010", "10000000000000000000100000000000000000000000000000", "00000000000000000000000000001001000000000000000000", "00000000000000000000000000010000000000000000100000", "00000000000000010000000000000000000000000001000000", "00000010000000000000000000000000000001000000000000", "00000001000000000000000000010000000000000000000000", "00000000010000000000000000000000000000000010000000", "00000000000001000000000000000000000000001000000000", "00000000000000001000000000000000000000000000010000", "00000000000010000000010000000000000000000000000000", "00000000000000000000000100000000000000000000000010", "00010000000000000000000000000010000000000000000000", "00000000000100000010000000000000000000000000000000", "01000100000000000000000000000000000000000000000000", "00000000000000000000000000000000010000000000000100", "00000000000000100000000010000000000000000000000000", "00000000000000000100000000000000100000000000000000", "00000000000000000100000000000100000000000000000000", "00000000000000000000000000001000000000000000000100", "00000000000001000000000000000000001000000000000000", "00000000000000000000000010000000000000000000000001", "00000000000000000000000000000000000000001000100000", "00000000000000000000000001000000000010000000000000", "00100000000000000000000000000000000000000000001000"}

Returns: 1
{"00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "11111111111111111111111101111111111111111111111111", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000", "00000000000000000000000010000000000000000000000000"}

Returns: 95
{"0100000000", "1010000000", "0101000000", "0010100100", "0001010000", "0000101000", "0000010000", "0001000011", "0000000100", "0000000100" }

Returns: 3
{"0100100", "1011000", "0100000", "0100000", "1000011", "0000100", "0000100" }

Returns: 5
{"011100", "100000", "100000", "100011", "000100", "000100" }

Returns: 3
{"010000", "101100", "010000", "010011", "000100", "000100" }

Returns: 3
{"0101010000", "1010000000", "0100000000", "1000001010", "0000010000", "1000100000", "0001000100", "0000001000", "0001000001", "0000000010" }

Returns: 3
{"010000", "101100", "010011", "010000", "001000", "001000" }

Returns: 3
{"01100000000000000000000000000000000000000000000000", "10000000000000000000000000000000000000000000000000", "10010010011111111111111111111111111111111111111111", "00101000000000000000000000000000000000000000000000", "00010100000000000000000000000000000000000000000000", "00001000000000000000000000000000000000000000000000", "00100001000000000000000000000000000000000000000000", "00000010100000000000000000000000000000000000000000", "00000001000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000" }

Returns: 85

Statistics

Problem Statement for "RoadsReorganization"

Problem Statement

Definition

Constraints

Examples