TopCoder Statistics - Problem Statement

Problem Statement

Elly's home has L lightbulbs. These are controlled by N switches. Each switch turns on a subset of the lightbulbs (possibly none or all of them).

Elly has numbered the lightbulbs 0 through L-1 in decreasing order of importance. For example, the lightbulb in the attic where she goes once per year has a much bigger number than the one in the living room.

Given two different sets of lightbulbs, A and B, we say that A is more important than B if and only if the most important lightbulb on which they differ is in A but not in B. For example, the set {1, 3, 9} is more important than the set {1, 4, 5, 6, 7} because of lightbulb 3.

The house electricity system has a serious flaw: whenever Elly uses a switch which is supposed to turn on a lightbulb that is already on, the bulb burns out and it can no longer be lit.

All lights are currently off. Elly wants to use some (possibly none or all) switches in such a way that in the end the most important set of bulbs will be lit. (Note that some of the bulbs that are not lit in the end may be burned out. Elly does not care about the number of bulbs that burn out.)

You are given the ints N and L, as well as a String[] switches which gives information on which lightbulbs are affected by which switch. Each switch corresponds to one element of switches, and character i of that element is '1' if said switch turns on bulb i, or '0' if it does not do that.

Return a String describing the most important set of lightbulbs Elly can light, with '1' representing a bulb that's on and '0' a bulb that's off. (That is, use '0' for bulbs that have never been turned on and also for bulbs that burned out.)

Definition

Class:: EllysLightbulbs
Method:: getMax
Parameters:: int, int, String[]
Returns:: String
Method signature:: String getMax(int N, int L, String[] switches)
(be sure your method is public)

Constraints

N will be between 1 and 50, inclusive.
L will be between 1 and 50, inclusive.
switches will contain exactly N elements.
Each element of switches will contain exactly L characters.
Each character in switches will be either '0' or '1'.

Examples

3

5

{"01101", "10110", "01011"}

Returns: "11101"

There are five lightbulbs and three switches: switch X controls bulbs {1, 2, 4}, switch Y controls {0, 2, 3}, and switch Z controls bulbs {1, 3, 4}. Given that we have 3 switches, there are 2^3 = 8 ways to toggle a subset of switches: Toggling just the switch Y gives us the result "10110". Toggling switches X+Y gives "11011" (with bulb 2 burned out). Toggling Y+Z gives "11101" (with bulb 3 burned out). This is the optimal solution. Toggling X+Y+Z gives "10000" (with all four bulbs that are off burned out). For each of the four remaining ways, bulb 0 will not be lit in the end, and therefore none of these is optimal.
10

20

{"00010111011100101010", "11110001010110011110", "00101010100100000100", "11000000111011101000", "01100101011001100100", "11010010110010000100", "01111111011000010001", "00001010111010011111", "11100011101000011011", "10001000011001001111"}

Returns: "11111101000011000110"
1

6

{"101010"}

Returns: "101010"
13

42

{"111100000101100000101010001000010000101011", "011010001001100000101000000110001111011110", "001101010001100011000100001100001011101001", "011110110101000101101110011011011111110110", "101011110011110111010010111011001110011011", "011001111111111001000001000010100010110011", "100100101000101111101100001011111111011111", "100111110111011000100101011110110001110001", "111110010001110111011011100010000000000100", "111000101001011000101001001101111101110110", "101110001000001110111111001011101001111001", "100100110110010000111100001110100011010101", "110011010001100000010001001001111000010111"}

Returns: "111110111111110000010100001000101100001011"
12

50

{"00000000000000000000000000000000000000000000000000", "01111111100011111100011111110001111111000111111110", "01111111100111111110011111111001111111100111111110", "01100000000110000000011000011001100001100000110000", "01100000000110000000011000011001100001100000110000", "01111110000111111100011111111001111111100000110000", "01111110000011111110011111110001111111000000110000", "01100000000000000110011000000001111000000000110000", "01100000000000000110011000000001101100000000110000", "01111111100111111110011000000001100110000000110000", "01111111100011111100011000000001100011100000110000", "00000000000000000000000000000000000000000000000000"}

Returns: "01111111100111111110011111111001111111100111111110"
13

45

{"000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000", "000111111111110000001111110000000011111000000", "000111111111110000011111111000000111111100000", "000000011100000000111000000000001100000110000", "000000011100000001111000000000011100000111000", "000000011100000001111000000000011100000111000", "000000011100000001111000000000011100000111000", "000000011100000000111000000000001100000110000", "000000011100000000011111111000000111111100000", "000000011100000000001111110000000011111000000", "000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000"}

Returns: "000111111111110000011111111000000111111100000"
1

1

{"0"}

Returns: "0"
1

1

{"1"}

Returns: "1"
50

50

{"10000000000000000000000000000000000000000000000001", "01000000000000000000000000000000000000000000000001", "00100000000000000000000000000000000000000000000001", "00010000000000000000000000000000000000000000000001", "00001000000000000000000000000000000000000000000001", "00000100000000000000000000000000000000000000000001", "00000010000000000000000000000000000000000000000001", "00000001000000000000000000000000000000000000000001", "00000000100000000000000000000000000000000000000001", "00000000010000000000000000000000000000000000000001", "00000000001000000000000000000000000000000000000001", "00000000000100000000000000000000000000000000000001", "00000000000010000000000000000000000000000000000001", "00000000000001000000000000000000000000000000000001", "00000000000000100000000000000000000000000000000001", "00000000000000010000000000000000000000000000000001", "00000000000000001000000000000000000000000000000001", "00000000000000000100000000000000000000000000000001", "00000000000000000010000000000000000000000000000001", "00000000000000000001000000000000000000000000000001", "00000000000000000000100000000000000000000000000001", "00000000000000000000010000000000000000000000000001", "00000000000000000000001000000000000000000000000001", "00000000000000000000000100000000000000000000000001", "00000000000000000000000010000000000000000000000001", "00000000000000000000000001000000000000000000000001", "00000000000000000000000000100000000000000000000001", "00000000000000000000000000010000000000000000000001", "00000000000000000000000000001000000000000000000001", "00000000000000000000000000000100000000000000000001", "00000000000000000000000000000010000000000000000001", "00000000000000000000000000000001000000000000000001", "00000000000000000000000000000000100000000000000001", "00000000000000000000000000000000010000000000000001", "00000000000000000000000000000000001000000000000001", "00000000000000000000000000000000000100000000000001", "00000000000000000000000000000000000010000000000001", "00000000000000000000000000000000000001000000000001", "00000000000000000000000000000000000000100000000001", "00000000000000000000000000000000000000010000000001", "00000000000000000000000000000000000000001000000001", "00000000000000000000000000000000000000000100000001", "00000000000000000000000000000000000000000010000001", "00000000000000000000000000000000000000000001000001", "00000000000000000000000000000000000000000000100001", "00000000000000000000000000000000000000000000010001", "00000000000000000000000000000000000000000000001001", "00000000000000000000000000000000000000000000000101", "00000000000000000000000000000000000000000000000011", "00000000000000000000000000000000000000000000000001"}

Returns: "11111111111111111111111111111111111111111111111110"
50

50

{"00000100000001010000100000000001000000111000000000", "11000000000000000000000000000000000000000000000000", "00101000100010100101000100000000100000001000000000", "00110000000000000000000000000000000000000000000000", "00101000001011100011000000000101000100100010111000", "00001100000000000000000000000000000000000000000000", "00010000000001101000010100100100011000000110100000", "00000011000000000000000000000000000000000000000000", "00100000101000000000100100010000100101100000000000", "00000000110000000000000000000000000000000000000000", "00000000000000010000000101000000000100001000000000", "00000000001100000000000000000000000000000000000000", "01000000101000000000000001000000000000001001010100", "00000000000011000000000000000000000000000000000000", "10000110000101010011101010000111011010000000000000", "00000000000000110000000000000000000000000000000000", "00100001000010000110000110100101100001000000001000", "00000000000000001100000000000000000000000000000000", "00000000000000000000100110000000000000000000000010", "00000000000000000011000000000000000000000000000000", "00000000000000000000000100101000000010100000100101", "00000000000000000000110000000000000000000000000000", "00000100010000000000000000001110000010000000101000", "00000000000000000000001100000000000000000000000000", "00010000010100001000001000000100001101001000100000", "00000000000000000000000011000000000000000000000000", "00100000000001000000010100101100100000000001010110", "00000000000000000000000000110000000000000000000000", "00000000010000001000100000000110000100000010000000", "00000000000000000000000000001100000000000000000000", "00000000100010000000000100000100101100000010001000", "00000000000000000000000000000011000000000000000000", "10000000000000000000000000001100000000100100000100", "00000000000000000000000000000000110000000000000000", "10100010000000000000000100000000001000100000000000", "00000000000000000000000000000000001100000000000000", "11110111000110000100000100001000011000100000000000", "00000000000000000000000000000000000011000000000000", "00000000000000010000000010000000100010000000010000", "00000000000000000000000000000000000000110000000000", "10000001000001000000010100111001000010000011000010", "00000000000000000000000000000000000000001100000000", "00000000101100100001000000100000000000000010000000", "00000000000000000000000000000000000000000011000000", "00000100000001010000000000000000100000010100100101", "00000000000000000000000000000000000000000000110000", "00010000001100001110000000001000000000000101000000", "00000000000000000000000000000000000000000000001100", "00000000000011001010000010010010100100101001001000", "00000000000000000000000000000000000000000000000011"}

Returns: "11111111111111111111111111111111111111111111111111"
50

50

{"11000000000000000000000000000000000000000000000000", "00010110000101010000000000000000100000000000000001", "00110000000000000000000000000000000000000000000000", "10101000001001010000000000000000001000000100000000", "00001100000000000000000000000000000000000000000000", "00000010000000000000100010000000000000000011010000", "00000011000000000000000000000000000000000000000000", "00001000000010000000011000100000000001000000100000", "00000000110000000000000000000000000000000000000000", "00101010000000100010100001011000000010000010000000", "00000000001100000000000000000000000000000000000000", "00100001000011000000100000100010100010111001000000", "00000000000011000000000000000000000000000000000000", "01000010000001000101000000100000000100010001000100", "00000000000000110000000000000000000000000000000000", "00000010000001000010001000000000000000010001000010", "00000000000000001100000000000000000000000000000000", "00100010100000001100000000000000000100000000000100", "00000000000000000011000000000000000000000000000000", "00000011100000000001001010000000001010010100101000", "00000000000000000000110000000000000000000000000000", "10000000001010000000011000000000000001000010000011", "00000000000000000000001100000000000000000000000000", "00000000000001001100000100000100000001000100001000", "00000000000000000000000011000000000000000000000000", "00100000000010100010100011100001001000000000000000", "00000000000000000000000000110000000000000000000000", "11100000010000101110010000000011000000000000000000", "00000000000000000000000000001100000000000000000000", "01001000001000000000001001100010000010110000000000", "00000000000000000000000000000011000000000000000000", "00111000000001000010010000100001001000001010100000", "00000000000000000000000000000000110000000000000000", "00001000000011000000000001000000011001110001000000", "00000000000000000000000000000000001100000000000000", "01000000000000000110000000000010000001001000001100", "00000000000000000000000000000000000011000000000000", "01000000000100101001000000000000000000000100010010", "00000000000000000000000000000000000000110000000000", "10001000101001000000010100010110000000000001000001", "00000000000000000000000000000000000000001100000000", "00001010010000100000000110100000000101101100010001", "00000000000000000000000000000000000000000011000000", "00111000010100010100001000000000010100101101000000", "00000000000000000000000000000000000000000000110000", "00000000100000111100000001010010000000001000000010", "00000000000000000000000000000000000000000000001100", "00011000001000000110000001000100000000100010000001", "00000000000000000000000000000000000000000000000011", "10100000000000001000100000000010101010000000001000"}

Returns: "11111111111111111111111111111111111111111111111111"
10

10

{"0000000000", "0000000000", "0000000000", "0000000000", "0000010000", "0000000000", "0000000000", "0000000000", "0000100000", "0000000000"}

Returns: "0000110000"
5

13

{"1110000110110", "0111110100111", "0000011101111", "1001101101001", "0100111100110"}

Returns: "1110011011001"
8

17

{"11000000011000111", "10100001010000011", "00000000000100000", "01110000010100110", "00000111000000100", "10011001110101001", "01110100001001001", "11010000100011101"}

Returns: "11101110100001011"
10

2

{"00", "00", "00", "00", "00", "00", "00", "10", "00", "00"}

Returns: "10"
17

13

{"0101000100000", "1100000000000", "0011011000000", "0001000001001", "1000000000001", "1000000000000", "0001000000000", "0001000100000", "0000100110001", "1000100010010", "0000010011010", "1111000110010", "0111101010001", "0000010000011", "0000000000011", "0101000101001", "0010010000011"}

Returns: "1111111110010"
22

33

{"110000000010000010000100000100000", "111000000000101000001000000110000", "000100000000000000000000000000000", "000001100000100000100000110100101", "100000100000000000000001000000000", "001010010000000010010100000000001", "000000010011001101000000100110100", "000000000001101000110001000000101", "000000010000000000100101001000010", "000000000000000000000101000000100", "100100000000000000000001000000000", "100001000000000010100100010000100", "000000010001000000000001000010010", "000011000110000101100101000000000", "000011010101000000000000100010000", "000000000000000001001000000000000", "000000000110000000000010000000110", "010000000010110000000011000000000", "001000000011000011100000000010000", "000000000000110000000000000000000", "111100000000000000000000100000000", "000000000110100000000000000010000"}

Returns: "111111110101110110001010001010110"
39

11

{"00000000000", "00000000000", "00000000000", "00000000000", "00000000000", "00000100000", "00000000000", "00000000000", "00000000000", "00000000000", "00001000000", "00000000000", "00000000000", "00000000000", "01000000000", "00000000001", "00000000000", "00000000000", "00000000000", "00000000000", "00001000000", "00000000000", "00000000000", "00100000000", "00000000000", "00000000000", "00000000000", "10000000000", "00000001000", "00000000100", "00000000000", "00000000000", "00000110000", "00000010000", "00000000000", "00000000001", "00000000000", "00000001100", "00000000000"}

Returns: "11101111101"
35

35

{"10000001000101101010100000001110000", "00110000110010011010010001000100010", "00000100100110000000111100000000000", "01101011000010100010110111011001000", "10000111111100010010101000100001110", "00010110010010100101100011000100110", "00010001000001000000000001101010010", "10100011010100000100001011100001011", "00011000011100011000000001001000101", "00000000011100100000011011100110000", "01000101010001000000000100001110010", "00111001000010001100111100000110010", "00000100101110111010110100110000000", "00110000010001001110000001110010010", "00100011001100111000011011110000001", "10000001110001101111010011000001100", "01110001110000000111100010011001001", "00100000001110010100001001100011100", "10011010110101101000010101011111000", "11001011101010001101010111100000000", "10000100100110001100100000000001000", "00111100011001010000000000000001000", "00000000000101111000001001011010000", "00000000011001000010010001000000000", "11100100010110111101011010100011100", "00000000000000011000110011011001001", "00000010100000001010111001010000000", "11100010000011101011110101100000001", "01010000010011001000000100010010100", "10000100100001100001001101010000100", "01001001001010011010001000100001011", "00100011101010111100011110110000000", "00100010110101101001100101011010100", "00000010001000001110000110100001100", "00100001101000101010011101011101110"}

Returns: "11111111110110000001110000000000000"
37

33

{"010110100100011111000111101010001", "111101011101101000110011111011011", "110101111011011110110111111001010", "100111101011011001111011001111101", "101100111110111111110111100111011", "111111111111111011110111011111011", "101111110111111111111011101011111", "111111101110010101001111111100110", "101111000111110011111010111010001", "111111011001110011111111101111010", "111111110111111101110101111101111", "111110111111110111011111110111111", "010111010011111111001111101111111", "111010011011111111111111101110100", "110111111101111111110111111111111", "101111001011101111101001111111000", "111111011110111101100100101111101", "110111111101111011001111101111011", "111111011111101111110110011111101", "111011101101111101001111110111111", "011111100110111010111011111011111", "101111110101011001011111010111010", "011001010110111111111011011110110", "101011011111101111001111101111111", "011110110101111101101101111110111", "111111101010011111001111110111111", "011100110111111111011111111101101", "111101111111110111001111011111111", "111011011110111101110111100101111", "111111110101111111101101100111111", "110010110011111110110111011111111", "111101010111110111111010110011011", "110101011111001111111011111111011", "101000011110101111111111111001111", "111101111111111111111111101111010", "111001010110011101110011001011111", "101001011111011111110110110101101"}

Returns: "111111111111111011110111011111011"
40

40

{"0000000000000000000000000000000010000001", "0000000000000010000000000000000000000000", "0000100000000000000000000000000000000000", "0000010000010000000000001000010000000000", "0000000000000000000000000000000000000100", "0001010000000000000000000000000000000100", "1010111000011000000000000000000000000000", "0000100110000000000000000000000001000000", "1000000000000010000000000000000100001010", "0001000000000000101000000000000001000000", "1001000000000001101000100000000000000000", "0000000000000000100010001000000001000000", "0000000000000010001000010000001000000000", "0010000001000000000000000000000000000000", "0001000000000000000000000000001000000000", "0000000000000000000000000000001100000010", "0000000000100011100000000010000000000000", "0000010000000000100001100001000010000100", "0000000000000100000010000000100000000100", "0000000100000000000000000000000100000010", "0000001000000000000000000000000000000100", "0000010000000100000000000000010000001000", "0000000000000000000001000000000000000000", "0000000000000000000000010010001000000000", "0000000010100000100000000000000000000000", "0001000000000010110000100001000000000100", "0000000001000110110100000000000001000000", "1000000010000000010000000110000000000000", "0001000011000000000000000000001100000001", "1000000001100000000000000000001100000000", "0000100000000000000000000000000000000000", "0000000000001000100000000100000100100000", "0000001100000010000001000001000000010000", "0000100001000000000000000000001011000000", "1100000001000000011000000000000000100000", "0100100000000000000000010000100101000001", "0000000000000000100000000000000001100001", "0000100000000000000000011111000000010000", "0000000000000000000000000000000000000000", "0000000000001011000000000000000000000000"}

Returns: "1111111111111111011011011000011010100000"
50

50

{"00000000000010000000000000000000000000000000000000", "00000010000000001000000000000000000000110000010000", "00000000000001000000000000000100000000000000000000", "00000100000000000000000000000000000000000100001000", "00010100000000000000000001000000000000000000000000", "00010000000000000000000000000000000000001000000000", "00000100001000000000000000000000000000000000000000", "00000011000000000000001100000000000000101000000000", "00000000000000000000000000000000000000000000000000", "01000000100000000000000000000000000000001000000000", "00000100000000000000001000000000000010000000001000", "00000000000000000000000000000010000000000000000000", "00001000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000100000001000", "00000000000000000000010000000000000000000000100000", "00000000000000000100000000000010000000000000000000", "00000000000000001000000000000000001000000000000010", "00100000000000000000000010000000010000000000000000", "00001000000000000001000000000100000000101000000000", "00000000000100000000000000000100000000000000000000", "00010000000000000000000000001000001000000000010010", "00000000001000000000100000000110000001010000000000", "00000000000000000000000000000000000000001010000000", "00000000000000000000000000000010100000000000000000", "00110000000000111000000000000000000010000000000000", "00000000001000000000000000000000010000000000000000", "00010000000000000000010100000000000000001000000000", "00100000000000000000000000000000000000001000000000", "10010100000000000000000000000100000000000000000000", "00000010000000000100000000000000000000000000000000", "00000000010000000000000000000000000001101000000000", "00000000000000000010000100000000001000000000000000", "00000000000000000000000000000000000000001000001000", "00000000000000000000000000001000000000000000000100", "10000000000000000000000000000001000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000010000001000100000000000000000000000000000", "00010000000000000000000000000010000000000000000000", "00000000000000100010000000000000000000000000000001", "00000000000000000100000100000000000000000000100000", "00000000001000000100000000000000000000000000000000", "00000000000000000000000000000000000000000000010000", "00010000100000000000000000000100000000000000000000", "00010000000000000100000000010000000000000000000100", "00000000000000000000000000000001000000000000000000", "00000000000000000000000000000000000000000000000000", "00100000000001000000000000000000000000000000001000", "00000000000000000000000000000000000000000000000000", "00000000001000100000000000000000000000010000000001", "00000100000011000000000000000000000010001000110000"}

Returns: "11111111111111111111111000001011001010010110011100"
50

50

{"00001000010000000000000000000000000000001010000000", "01000010000000000100000000000000000110000000001000", "00100000000101000000000001000000001000000000100000", "00000000000000000000000000000000000000000011001000", "00000001010000000000000010000000000000000010000000", "00000000100000000100100000000000000000000001000000", "00000010000100000101000000000100000010000010100010", "00010000010000001000100000010011001000000000000000", "10001000110000000000000001000100000000000000000000", "00110000000000000100000000000100000000000000000000", "00000000010010000001000001000000000000000000000000", "00000000010000000000000000000001101010010000100000", "00010000001000000000010000000011000100100000001110", "00000000000000010010001001000000000000000000100000", "00000000000000000000010000000000000000000000001101", "00000100000100000000000110000000000000010100000000", "00000000001100000010000000010001000010000000010000", "10000000000000000000000000000100001000010000000000", "01000001001000000000000000000000011000000000010000", "00000000010000000110000100000000000000001000001000", "00000001001000000000000000000000000000000000000000", "00000000000000000000001000001000100101000000000000", "00000000000000010000010000000000000010000000000000", "00000000010000000000010000000000100010000000000000", "00000000000000000000000100100000000000000000100000", "00000000100000000000000000000000010000000000000000", "00000000000010000000000000000001000000000000000000", "00000000000000001000000000000000000100001000100000", "00000000100100000000000000010100000000000000000000", "00000000100010000000000100000000000000001000010000", "01000001001000000000000000000000000000000000100100", "00000000000001000000000000000100000000000001000000", "00000100000000000000000001000000000000000000000000", "00000000000000000000000000000000000000000100000011", "00001010000000011000000000000000110000000000000000", "01000000010000000001001000000001001000000000100000", "00000000000000000000000000000000000000100000000000", "10000000000000000000000100000000000000000001000011", "01101000000100000000000000000000000000000000000000", "01000000000000000000010010000000000000000000000010", "10000000100001000100011101000000000010000000000000", "00000000100000000000000010001000000000000000000011", "00000000000100000101100001100100000010000000001000", "00000001000010000000000000000000100000000000000001", "00000000000000000000000000100000000000000000000000", "01100000001000100100001010000000000100000010000000", "00000001000100000000000001001000100000000000000000", "01000000000100000000010000000000000000101000000000", "00001000000001001110000000000000000101000000001000", "00001000000000000000000000000000101000001000000100"}

Returns: "11111111111111111011110110111111000001101101001100"
50

50

{"00000000001000000000000001010000100000000100100000", "00100000000000010000011011001101011100000010101000", "01100000001000000000000000010101000100000000000010", "01000100000001010000000101100000010100100000001001", "01001010001100001001000000101000001000110011010000", "00000100011000000000000001010000100000001000000000", "00000000010010000001001010110011010100010001000000", "00011000000001001100000001001000100010100011100000", "11010000000100000000000000000110000001100000000000", "00000000100000000000000000000000110000010000000010", "00000000001010110101000000000000000000101000101001", "00100000110000000000000000010000010000101000011100", "00000000000000000101000100000000010010000000000001", "00000011000000001000000000010110001000001110001100", "11100000001000000011100010000000000000000000010010", "00000000011101000001000000000010100001100000010010", "00001000011000000000000010000100000000000101000000", "11001010100010000001101000000001001010000101100000", "01010001000101011000100100001000000010000000100000", "00001000101110000011000010010101000100011000000100", "00001000100000011000000000010000000100000010000000", "10000101000000000001000100010000001000010101001010", "10000001001000010000000010000000100100000010010010", "00001000000000010010000000100000000000000010001000", "00011011000100000001000001010000100011010010101010", "00000000000101000001000000100010000000110001000000", "00100010010001000000000000001000100001000001000000", "10000000101001000101001000001010000000001001111000", "00000010110001000001100000000000010000000000001001", "10011010000001001000100000010000000000000000110010", "00000010000100000000001000000010000010011000010000", "10001011001000000011010001000000100000000010000011", "01100000000000000010100000010011000100000000001000", "10000000001000000100010010010000010000100000000000", "10000001000110000001000000100011010010010000000000", "00000100000000010000100000001100001000000000000000", "00010100001001000000100001100000010100000100000001", "00010000000000000000100001000110010000000000101000", "00010000000001001100000000000000000000000001010000", "00000000000000001000000000000000010010000001001010", "00110100010000010001110000000001000001000000000010", "00000000001000000000000000100110010111000110100110", "00000000001110110000000000011000100100001001000001", "10001000000001100100101000010000010000100000000100", "00000011000100000000110100000000000100000000010100", "10000000000101010101001000001000010010001010000101", "00100001010000010010000000111000000001000010000000", "00000000000100100000100000000000000000101101000001", "01010001000010000100010000010010100100010000101010", "01111000001000010000000100010000010000000010010100"}

Returns: "11111111111111111111010111001000101001100110010000"
50

50

{"00000001100000110001000000010000010001110100001000", "01101001101010011001101001101001000010000000001101", "10000101101000000000000010000100010101001010000011", "00010000011010010100000010001000100001000000100100", "11011010101100100000000010000111100000100010100010", "01011000011100010100100000100111000011010000100101", "01001100000000101000100100010010011101110000000010", "01101011011000010100010010010110001000010011000000", "11000001001010000001100100110110001100100101110000", "10011000000001100010001001001011111010011100100110", "10011100001010010001110001100111101001000000010110", "00010000000100110110000000101000100101100001000010", "11100101001101000100000000000010101010101011010000", "10000000000110010000001110000100101100101100010000", "11001100100010101111000101000010001010000000110000", "01000010000100000010110000001000000001011100001000", "00001001100011010101011000100001010110000110100000", "10110010001000011001100000010100101100001001010000", "00000000011000010100000000000010000110100010001000", "11000011000001110000110010000100000101000000110110", "10101001100000010000110000011000110000010000100100", "00001000001001100010010000110010010001000000101110", "11100001001101000000100111010100001110010010000101", "10001000010001000010000010110110110010010100001111", "01000110000000010101100000100001000010011000000000", "10001011010010010101000100100010011001001101011001", "00010100011001111101001011100010000000001011000100", "00100011001000001110101000111000010000011100100101", "10100000101000001001000100000000011000100100011001", "10101010000100100100001000011010000000101100111001", "01001010001000010010110000110000100000010001101101", "00010110000101101110001100110010010011100010000000", "11011010001100000000100110011000100000000111000000", "00000000100010011000000001101110001000000001010101", "01000000011000011000010000000011011010000000000011", "00000100101100000010000011000011100100111110100010", "00110001110100011100011000010000001000010100011000", "00000100001101000100000000000001000100001000010001", "00000010000000100010000000101011100101111101111100", "00011100010011100010001110101100000000001001011000", "00010000110100110001100000100101111001010001101101", "10100011000000010100000100010011010010000000101001", "10000010001010010011001111000000011000000000001000", "01001000100001000000010000000101110000000000001110", "00111010110001000010101100000000011110011101101000", "00010010001100011001000001000001011000000000000000", "10000001000001000010000111001000000010000100000000", "00010100000110010100000101010011010011001001111100", "11110110010110111110111010010101001000100000111000", "11100000111110011000100101000101010000110010011000"}

Returns: "11111111111111001101101010100111001000010100010110"
50

50

{"11110010010111001011100100001101100111101110000110", "10111100001110111010110100100010110001111011001000", "00110111001101110010111000011011110010100001010111", "11010001111110000101101010010011111010111010011101", "00001110010111000111000111001011111101011010010011", "01111011100000010100000000001000010110011110000000", "00001000110001000001100000101100011010000000011011", "11100101110101011000010101000000000011001001001100", "10010111000000100101001011011110010011010101011011", "10011011101001100110100100110111000000010001111101", "11111001111000101111000000111110010010010010010100", "10011011110111101001110000110100011000000101011110", "11011101101111110010101101011011001000110011110110", "01001010111111100101110011111110101010101110110001", "01111010001011000001000000011011111110000110011010", "10101111110000011101101110110011111101110100010111", "00110000101000011010110110100000000111010101100101", "10110111100000101110110110101101101011100111100001", "01111100111100011101101011101010011011111100001111", "01110000111000000011110000000001110010110010101111", "10111000100100000001010001101110001100100101000010", "01001101011000101101100000110011111000100101100110", "11110001011111101101110010010110001100000101100101", "11001111011010001110010100011010000101101101010001", "11001111100011100000100101110100111010010000110111", "01011011110101111011000111000110010000101001100011", "01101101110010100111000101011000111011101110001000", "00001011111010001100010011100110011010000111000110", "00011010100111110010011011010000111111110110100100", "11100010111110100110101100101101100010101001001000", "11010100110101000111001110111000001101110000001100", "01100110100111101111111100101011000000100111011010", "10110101111010011101000111110100101100000001100101", "10001101011001111011110111010101110110011100101100", "00111000011100111110100011000101101101001101101011", "00010010010000010011010011111010000100110110101011", "00010111111101110001110101100000010001101001010101", "10111110101101011100001101111011111000001010100100", "11011110011001001001000000000101011110010010101100", "11101001110010101100000111111101110110110000100000", "01101000111011010011011110100011010111001101101101", "11001101111110000011010100110001001100011010111110", "11100000110010100010111110010011001110111001101000", "00100100100101111010101100001110111011111111000010", "10000000000101101011110111011111100011100101000101", "10101110000111000101100111101110010100001100011001", "11010111100111111011101011000100011111101101011100", "00111100000001100000011001100111010011111111101000", "10000010101000011110010001110100100010110100101101", "01001001011111010010110010001001011110000000000010"}

Returns: "11111111111011110110010101111101000100011000110110"
8

42

{"010101010101111111101010100100100101010010", "000010101000101010001011101000101001010011", "010010101110101110111111100101000101011110", "010100110101111111111111000101000000000101", "010011111110100010000000000010111000101010", "010110110100100111000010001001010001011101", "110001011101000010111011100000110001010001", "100011010001010100101011010110000101010011"}

Returns: "110111100100101011010100010011000101010110"
4

10

{"1001100000", "0101010000", "1001001000", "0001000100"}

Returns: "1100110100"
5

10

{"1001100000", "0101010000", "1001001000", "0001000010", "0000000110"}

Returns: "1100110110"
30

50

{"11110010111011111111100000000010100111010110101010", "11101111110110001001110001101100101110001100111100", "00101111011100100101101110110111001110100001001011", "11101010000000110111000101111110000101100101001001", "10010010101111010001011111010111110111110110111101", "10011100110101111110000101001011111001001110000011", "01000111010001011000110110010100111000011000001101", "00110000000110000111110110010110001101100000001101", "01001011000001100110111101000011010110100011110110", "10100011001011101111011100101000011100100010100101", "10101100001000001101101101100110100111111011110100", "10101110111101010100010101010000011100110100011001", "01110001010011011101101011010111100011110110000010", "01011001010001010110101001100100001000011100100000", "01000010001010111100100011100101010010110001111011", "11000011001101110111101010110111111111101101100101", "11111100101000011000010110100100000011000001100010", "01110111010001110100101010000011110001011101000100", "10110100101110111101011001110101100101110011010010", "10001000011001000011100101111010111110011000111011", "10111101011011100001110101110000011001100001011001", "00011000011101001101100011000001011011110111011110", "00111100011100000000000100000111011000001111010100", "11111001001011101100000101101100111010110011001101", "11110011100101110110100110010101111101000111000100", "00100101111011111101011011110100011001011001010100", "01010111010110101110010000000101001001001100100010", "11001110001000110111010000110000111110101000100000", "10101010000100011000011010010011101111100000011001", "01101000100010101111011000010101110110010101101000"}

Returns: "11111111101111011011100100110110110011010000100100"
50

50

{"10000000000000000000000001000100000010010010001000", "10000000000000000000000011000000000000000010001000", "10000000000000000000000100010100001000100100000010", "01000000000000000000001010000100000100000101100001", "01000000000000000000000100110000000000001001000000", "00100000000000000000000000000000001000000010010101", "00100000000000000000011100101000001000100000000100", "00100000000000000000000100000000100000000001010000", "00010000000000000000011000010000001000000100000010", "00010000000000000000000000000000000000101000001000", "00001000000000000000000010001000000010100000001000", "00001000000000000000000100000000011000000001010011", "00001000000000000000001000000001010000100010100011", "00000100000000000000000000101000000000001010000110", "00000100000000000000000000000101000001101000100000", "00000010000000000000100010101000100000000000000001", "00000010000000000000000010001001000010000000000000", "00000010000000000000000001000000100110100001101010", "00000001000000000000001000000000001000100000000110", "00000001000000000000000010000000000000000000000010", "00000000100000000000100000001010100100000110000000", "00000000100000000000000000100110000000001010010000", "00000000100000000000000011010000000100001001010010", "00000000010000000000010000100100000011001001000000", "00000000010000000000000000000000011101000000010011", "00000000001000000000100011000010100000000000000000", "00000000001000000000000010101000010000100000000000", "00000000001000000000010000010000101000000000010101", "00000000000100000000100001110000000000111110100100", "00000000000100000000000100001000000100000000000100", "00000000000010000000011000000000000000000000010000", "00000000000010000000010001111000100000000000000000", "00000000000010000000000110000000100100000010010111", "00000000000001000000000001010010100100000000000101", "00000000000001000000000001100010111001100011000000", "00000000000000100000000101010000001011101011000000", "00000000000000100000100011100000000000000000010010", "00000000000000100000000000000000000000000000000100", "00000000000000010000101000000100000001000100000000", "00000000000000010000010000000000100100001100000010", "00000000000000001000000000000001011000000000000000", "00000000000000001000000010100000001000011000000000", "00000000000000001000100100000000000100001100000000", "00000000000000000100100000010100000000000000100000", "00000000000000000100101010000000100000000100011010", "00000000000000000010000010100000000000100100000100", "00000000000000000010010001000010001110100001000000", "00000000000000000010010100000000100101001010000100", "00000000000000000001110001000000100011110000000001", "00000000000000000001101000000000001100100110010000"}

Returns: "11111111111111111111011001000001000011010000101000"
33

50

{"01000111011000111110010100000000001111110110101110", "10000010001011010110111110000000010110001110101100", "11111110110101100100001000111101001001110110011011", "10000101110111010001100000111001001110111110010001", "01000001001100101001001000000100111111110100010001", "11011011000010011011000000000010010111100111100000", "10000111010101011000111110111011001011000000101110", "10001000000000101111010011110101010010100110000000", "00001100010110100010110100111011111011010110101100", "11011010010101011011001011101011110000101110110111", "10001010110111101111010101110011000000111011011001", "01100100000000000111101010111010001100001011101010", "11110000001011101110000111000111010100011110111000", "10101100110110001011000110001001110111010101001000", "01111111001100100101011011001001011101100100010001", "11000010000100101011001100100000001000000111001111", "00111110011110100010011010101010101011011000001000", "00110101100101000100010011111010010111100110000111", "01001111010010000010100111101100010110011010101010", "11110010000000101101100111101000110111111111000001", "00111110000100010010011000101001000111000011111101", "10011010010010110010100101010110010100000010000011", "00011010101000101110001000011011011100010111011110", "10100000000010011100001100001110101010100110100011", "11110011011101111111111110110110100100101010011101", "01001110000010000001001001011111001011000111100111", "11000110000000000101010111111110001100110101100010", "01101011000010111000001101000000001011000101010000", "10011110111001111001010110101001101010000101000001", "00000100011110110001010011001000010110111001101011", "00010000101110010111100101100010110001101000000110", "00110101111101011000001110110010001001011101111110", "11001010010101100011011101111001100000101101110000"}

Returns: "11111111111100001001001010000000001101010100001101"
42

50

{"01000100010000101110101111111100111010000011111011", "01010110000000011011110101110101010010111111111110", "01111111101011010110101001101110000000001011100001", "00000101010011101001100111000000100010010000011100", "01001011100000001010001111010011111111011010010000", "10100001100100011100111101010111101000010001111001", "00011011111010010001101111001100101100110101000110", "10011011001001001100111101101011100100000011011110", "11001111110110000111111010010101011111000101100101", "11110011001010101001010101010111010101001001000101", "00010010110101101111101010011101000110010101010110", "01010111111000111100100101011110111010100101110011", "01110001110111100100110101010001001100111110100010", "01001000111001001100011110111110010110011101110110", "11010011110101110111101000000100011010010110010001", "10111110001101000110000110011000111001101101000000", "01001110100001100010011011010100010100100100001101", "01000000101011100101011010110001011001100000111100", "01100110010001111111000000011001001010111010000110", "01010010100010000110100011111111101111111111100110", "10000010110010011010001111100001010110000100100000", "10000010110000100000011000101000011001111010111110", "01101101100010000001100011111111100001101010110100", "00111010111011010100100000010011111110010001101000", "01110101000111101100010001011001001101000100011111", "01110110100000100101110001000110000111100010110001", "01011011010100111110100100001011011101110100000010", "11011110101101110101001100101111010101001111010010", "00011110011101110000000011001000111110100110001111", "10100011100000011110010111011100100000000001101100", "01100011110000110010100000001111100101100010111001", "00011010000111000101111110011011011100011011111010", "10101010100110100010011110000100100000011001000101", "01101010010010011001101000001111000010011110010001", "01000101110000111010100111101110010100001110111000", "11100100001000011000000101101111110111010100110100", "00010010111000101010001100111010101111101110101101", "00101100001101111001000111011011000111001100001011", "10000100101111111100001010001011000101100111010110", "10010010001011000100000110000101101111001000001000", "01111010000011110101001001011100010110100000111000", "10110010100101011010001100100101010010101111001110"}

Returns: "11111111111000001110101111011111011101011010011010"
50

50

{"00000000000001000000101000011110100101010111001000", "10000000000000000010011000010110111111011101111001", "00001000000000000001000010110011010001010001111111", "00000000000000100011100001100001011011001001100001", "00000000000000010001101000110101101011000101111100", "01000000000000000000110000000001010011110110011101", "00000000100000000010011110110110101100011101110110", "00000000100000000000110001111001011010110001011010", "00000000000001000000111011000110111010110011000011", "10000000000000000001101110000101011111101101110001", "00000000000100000010011011111101110010011011010110", "00000000001000000000100000011000000011101111011001", "00000000000010000011010001010011011011110000100110", "00000000100000000010000000111001111000111111100010", "00000000000100000010010001111110011101100101111101", "01000000000000000010000000111001111001110001010010", "00000100000000000011010111001010000000110111110111", "00100000000000000011000111110001111001110000110010", "10000000000000000011000010100100110111110001001101", "00000001000000000001111101100101100110110011011111", "00010000000000000011100111010011111111011000000100", "00000000010000000001011000110100111111111110010111", "00000000000000100000001101100010011110101000111111", "00000000000000001001111011111000001100000011000110", "00000000001000000010110001100111001011000010010100", "00000000000000010010010000010111101100111100101100", "00010000000000000010101010010110111000001011101101", "00001000000000000011010011110011001010100010000110", "00000000000000001000101101011010001111111111010010", "00100000000000000011000101101011000001101010011100", "00000000010000000001010010001111111001010110000111", "00000000000010000011001110011000011000011011000111", "00000000000100000011000011101101011000100100000100", "00010000000000000000011010100000011011000001011100", "00000001000000000010010110111011100110010100111101", "00000100000000000010011111010001000100100011000000", "00000000000000010011010110111100001100110000001011", "00000000000000100010110111100011111111011000100100", "00000000000010000001110000000100000110000010001101", "00000010000000000001010000011110000111000000111101", "00100000000000000000100110000111010110011010000010", "00000010000000000001111100100010011011011101110000", "01000000000000000010111011111111101110001110010001", "00000100000000000001100100001111111010000111110000", "00000000010000000001001110111010001100011100111010", "00000000001000000011111101010111111110111101111010", "00001000000000000000111000100101110000110010001001", "00000001000000000011100110110110011100110111110101", "00000000000001000010110100000110110011010010101011", "00000010000000000010001101110111001011001110101000"}

Returns: "11111111111111111010000000000000000000000000000000"
50

50

{"10100000000000000000000000000000000000000000000000", "01101000000000000000000000000000000000000000000000", "00011010000000000000000000000000000000000000000000", "00000110100000000000000000000000000000000000000000", "00000001101000000000000000000000000000000000000000", "00000000011010000000000000000000000000000000000000", "00000000000110100000000000000000000000000000000000", "00000000000001101000000000000000000000000000000000", "00000000000000011010000000000000000000000000000000", "00000000000000000110100000000000000000000000000000", "00000000000000000001101000000000000000000000000000", "00000000000000000000011010000000000000000000000000", "00000000000000000000000110100000000000000000000000", "00000000000000000000000001101000000000000000000000", "00000000000000000000000000011010000000000000000000", "00000000000000000000000000000110100000000000000000", "00000000000000000000000000000001101000000000000000", "00000000000000000000000000000000011010000000000000", "00101010101010101010101010101010101010101011011111", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010111101111101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110111010101", "00101010101010101010101010101010101010111101110111", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101000101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010100110110101", "00101010101010101010101010101010101010110101010111", "00101010101010101010101010101010101010110101110111", "00101010101010101010101010101010101010110100110111", "00101010101010101010101010101010101010110101100111", "00101010101010101010101010101010101010001101110101", "00101010101010101010101010101010101010100101110101", "00101010101010101010101010101010101010100101110101", "00101010101010101010101010101010101010100101110101", "00101010101010101010101010101010101010010101110101", "00101010101010101010101010101010101010011101111101", "00101010101010101010101010101010101010010101110101", "00101010101010101010101010101010101010101101010101", "00101010101010101010101010101010101010101100010101", "00101010101010101010101010101010101010101100001101", "00101010101010101010101010101010101010100001110101", "00101010101010101010101010101010101010111000101101", "00101010101010101010101010101010101010110101101101", "00101010101010101010101010101010101010100101011001", "00101010101010101010101010101010101010101010110110", "00101010101010101010101010101010101010110101010100", "00101010101010101010101010101010101010110101110111", "00101010101010101010101010101010101010110101010101"}

Returns: "11010101010101010101010101010101010010000000000000"
50

50

{"10000000000000000001000000010000011010001000000001", "10000000000000000000000000001010010000000000001010", "10000000000000000000000001001010000000100000001110", "01000000000000000000000110000101000000010000010011", "01000000000000000000000101101001000101000000100000", "01000000000000000000000000011001000000000000000000", "00100000000000000000000000001001100000110100100001", "00100000000000000000000101000100000000000010001000", "00010000000000000001000100000000000000000000000001", "00010000000000000000110010001110100000000100100000", "00010000000000000000000100000000110001000000000101", "00001000000000000001000010000010011001000010000000", "00001000000000000000011100000100000101010000000101", "00001000000000000000001000000000111010000010000000", "00000100000000000000000001000000000000100000010000", "00000100000000000000000000000000000100001000100000", "00000010000000000001010010000001000100101000000100", "00000010000000000000010100000000001100010000100000", "00000010000000000000000010011000000000000101000000", "00000001000000000000000110000010000000010000010010", "00000001000000000000001000000001000011000010001000", "00000001000000000000010010000010001010000000000000", "00000000100000000000000110000011000000010000011010", "00000000100000000001010001000100000000010000000000", "00000000010000000000000000000100001000000100001010", "00000000010000000000010000010011000010000000100000", "00000000010000000001010000100100001000000000101000", "00000000001000000000010010111000010011000100001010", "00000000001000000000000100000100010000000000000000", "00000000001000000001001000000001001000000010000000", "00000000000100000000100100101011010001100000100000", "00000000000100000000010100000000000001000000010000", "00000000000010000000110100001000000111010000000000", "00000000000010000000000000010001000000000000010000", "00000000000010000000100000011000110001000000000000", "00000000000001000000000000000100100000010001000000", "00000000000001000000000100000001100101010010010000", "00000000000001000001010010000000000100100000100001", "00000000000000100000000000000001000000000000010001", "00000000000000100001100000000000000000100000000000", "00000000000000010000000110001010000000101110111000", "00000000000000010000000001100000000001001100000001", "00000000000000010000000000100000100011000001000010", "00000000000000001000000010000001100100000000110000", "00000000000000001001000110000000000101000000000000", "00000000000000001000000000000100000000000011000000", "00000000000000000100000000000000100000000010001000", "00000000000000000101001000000010000100001001100000", "00000000000000000010000000110010000001000100000010", "00000000000000000010011000000001001000000000011000"}

Returns: "11111111111111111111111001100000000110100000000100"
50

50

{"10100000000000000000000000000000000000000000000000", "10100000000000000000000000000000000000000000000000", "10100000000000000000000000000000000000000000000000", "01101000000000000000000000000000000000000000000000", "01101000000000000000000000000000000000000000000000", "01101000000000000000000000000000000000000000000000", "00011010000000000000000000000000000000000000000000", "00011010000000000000000000000000000000000000000000", "00011010000000000000000000000000000000000000000000", "00000110100000000000000000000000000000000000000000", "00000110100000000000000000000000000000000000000000", "00000110100000000000000000000000000000000000000000", "00000001101000000000000000000000000000000000000000", "00000001101000000000000000000000000000000000000000", "00000001101000000000000000000000000000000000000000", "00000000011010000000000000000000000000000000000000", "00000000011010000000000000000000000000000000000000", "00000000011010000000000000000000000000000000000000", "00000000000110100000000000000000000000000000000000", "00000000000110100000000000000000000000000000000000", "00000000000110100000000000000000000000000000000000", "00000000000001101000000000000000000000000000000000", "00000000000001101000000000000000000000000000000000", "00000000000001101000000000000000000000000000000000", "00000000000000011010000000000000000000000000000000", "00000000000000011010000000000000000000000000000000", "00000000000000011010000000000000000000000000000000", "00000000000000000110100000000000000000000000000000", "00000000000000000110100000000000000000000000000000", "00000000000000000110100000000000000000000000000000", "00000000000000000001101000000000000000000000000000", "00000000000000000000011010000000000000000000000000", "00000000000000000000000110100000000000000000000000", "00000000000000000000000001101000000000000000000000", "00000000000000000000000000011010000000000000000000", "00000000000000000000000000000110100000000000000000", "00000000000000000000000000000001101000000000000000", "00000000000000000000000000000000011010000000000000", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101", "00101010101010101010101010101010101010110101110101"}

Returns: "11010101010101010101010101010101010010000000000000"
50

42

{"000000000000010000000000000000000000000000", "100000000000000000000000100000010000000000", "000010000000000000000001000000000000000000", "000000000000001000000001000000000000000000", "000000000000000100000000100000000000001000", "010000000000000000110000000000001000000000", "000000001000000000010000010000000100000000", "000000001000000000110000000000000000000000", "000000000000010000010000001000000000000000", "100000000000000000000000010100000000000100", "000000000001000000000001000000000010000001", "000000000010000000000001010001000100000100", "000000000000100000000000100000001000000010", "000000001000000000001100000001000001000000", "000000000001000000000011100000000000000100", "010000000000000000000001010000100001100000", "000001000000000000000010000000000000000000", "001000000000000000000000000000000000000000", "100000000000000000000000000000100010000001", "000000010000000000000000000000000100000000", "000100000000000000000000000000000000000000", "000000000100000000001001100000000000000000", "000000000000001000000000000000001000000000", "000000000000000010000001000000001000000010", "000000000010000000000000100010000000000100", "000000000000000100000010000000000100000000", "000100000000000000000100000000000000101000", "000010000000000000001010000000000000000100", "000000000000000010010000000000000000000000", "001000000000000000000000000000001000000000", "000000000100000000000000001100000000000000", "000000000000100000000000010000001000100000", "000000000001000000000000000000000000000100", "000100000000000000000000000000000000000010", "000000010000000000001000000000000000000000", "000001000000000000000000001000000000000010", "000000000000000100001000000000100000010000", "000000000000001000000000000100000000000000", "000000000000100000100000000010001000001110", "000000100000000000000000000000000100000100", "001000000000000000000000000000001000000000", "000000100000000000000000100001000000001000", "010000000000000000000001000000000000000000", "000001000000000000000000000000000000010000", "000000000100000000100000000000001100001000", "000000000010000000000000000000000000010000", "000010000000000000000000010010000001000000", "000000010000000000000010010000001000110000", "000000000000010000000000110100000000001001", "000000100000000000000000000000001000000000"}

Returns: "111111111111111110111111111111100010011101"
50

50

{"10111111111111111111111111000010000000000100000000", "01111111111111111111111111000001001000000010001000", "00100000000000000000000000000001000000000000010100", "00100000000000000000000000000000000000001000100000", "00010000000000000000000000000000001000100100001011", "00010000000000000000000000000001100000000001000001", "00001000000000000000000000000000110000001000000101", "00001000000000000000000000000000011000000000000001", "00000100000000000000000000100100000000000001110000", "00000100000000000000000000010001010001010000001000", "00000010000000000000000000000000001000000101010101", "00000010000000000000000000000100010010010000000010", "00000001000000000000000000000010100000001000000010", "00000001000000000000000000110100000100001100000000", "00000000100000000000000000000000000000010000100000", "00000000100000000000000000000010001111010000000011", "00000000010000000000000000000000000000000000001000", "00000000010000000000000000000000100000000000101000", "00000000001000000000000000000110001000000100000000", "00000000001000000000000000000000110000100000000000", "00000000000100000000000000000000010010001000000000", "00000000000100000000000000000000101100000000000001", "00000000000010000000000000000000100000000001000000", "00000000000010000000000000001000100000001010000000", "00000000000001000000000000101010000000010000010001", "00000000000001000000000000000000010000000000000000", "00000000000000100000000000010010000010100010000110", "00000000000000100000000000000000001000010000001000", "00000000000000010000000000000000001000010000000010", "00000000000000010000000000100000100000000000000000", "00000000000000001000000000110000000000000010001000", "00000000000000001000000000000000100010001001000100", "00000000000000000100000000000000000000110100000010", "00000000000000000100000000000000000000001001000010", "00000000000000000010000000001000000000000010100100", "00000000000000000010000000100000000000001000000011", "00000000000000000001000000000010000101000000100100", "00000000000000000001000000010000000001000000100000", "00000000000000000000100000001100100000111000001001", "00000000000000000000100000000000010000010000000000", "00000000000000000000010000000000110110000000010001", "00000000000000000000010000100100000001100100010000", "00000000000000000000001000010000000000000000011000", "00000000000000000000001000000001000011000010001000", "00000000000000000000000100000000110100100000000110", "00000000000000000000000100000000101011000000100000", "00000000000000000000000010001000010100000010000100", "00000000000000000000000010000000100111000000010010", "00000000000000000000000001010000000000100110000000", "00000000000000000000000001000100101001000011100101"}

Returns: "11000000000000000000000000111111111111111001100000"
50

50

{"10101010101010101010101010101010101000000000000010", "10101010101010101010101010101010101000000000000111", "10101010101010101010101010101010101000000000001000", "01101010101010101010101010101010101000000100110000", "01101010101010101010101010101010101000000000000001", "01101010101010101010101010101010101000000000100000", "00111010101010101010101010101010101001000000100000", "00111010101010101010101010101010101000000000000010", "00111010101010101010101010101010101000000000000000", "00101110101010101010101010101010101000000000000000", "00101110101010101010101010101010101000000010000000", "00101110101010101010101010101010101000000000000000", "00101011101010101010101010101010101010000000010010", "00101011101010101010101010101010101000000000000000", "00101011101010101010101010101010101000000000000000", "00101010111010101010101010101010101000000000001000", "00101010111010101010101010101010101000000000000000", "00101010111010101010101010101010101000000001000000", "00101010101110101010101010101010101000000100000000", "00101010101110101010101010101010101010100000001000", "00101010101110101010101010101010101000000000000000", "00101010101011101010101010101010101000000000000000", "00101010101011101010101010101010101000000000000000", "00101010101011101010101010101010101000000000000000", "00101010101010111010101010101010101010010000010000", "00101010101010111010101010101010101001000000010000", "00101010101010111010101010101010101000000110000000", "00101010101010101110101010101010101001010000000000", "00101010101010101110101010101010101000001000100000", "00101010101010101110101010101010101000000000010000", "00101010101010101011101010101010101000000000001000", "00101010101010101011101010101010101000000100000000", "00101010101010101011101010101010101000010000001000", "00101010101010101010111010101010101001000000000000", "00101010101010101010111010101010101011000000000000", "00101010101010101010111010101010101000000001000100", "00101010101010101010101110101010101000010001000000", "00101010101010101010101110101010101000110000000000", "00101010101010101010101110101010101001000000000000", "00101010101010101010101011101010101000000100010000", "00101010101010101010101011101010101000000000000000", "00101010101010101010101011101010101010100000000000", "00101010101010101010101010111010101000001000000000", "00101010101010101010101010111010101010100100010000", "00101010101010101010101010101110101000000000100000", "00101010101010101010101010101110101001100000001000", "00101010101010101010101010101011101000000000100000", "00101010101010101010101010101011101000001000000000", "00101010101010101010101010101010111100001000000000", "00101010101010101010101010101010101100000010000000"}

Returns: "11010101010101010101010101010101010111111110001111"
50

50

{"10000000000000000000000001000000001000001010100001", "10000000000000000000000000001000000000010101000110", "01000000000000000000000000101000000000000010011000", "01000000000000000000000001000000000010000000000000", "00100000000000000000000000100000001100000000011010", "00100000000000000000000001000000000100000100001000", "00010000000000000000000001000000010100001000111100", "00010000000000000000000000001001000101000000001011", "00001000000000000000000000000000001000000010000100", "00001000000000000000000001100000000010000000000100", "00000100000000000000000000001000000100100000000110", "00000100000000000000000000001000100010000000100000", "00000010000000000000000000000100000001000101100010", "00000010000000000000000001110000001110000001100000", "00000001000000000000000001000000000100000100000000", "00000001000000000000000000110000000100000000000010", "00000000100000000000000001000100000000001000100000", "00000000100000000000000000001000000000000001000000", "00000000010000000000000000010000001100000000000000", "00000000010000000000000000000100010000000000000000", "00000000001000000000000000100011010011001000010000", "00000000001000000000000000001101001000000001010100", "00000000000100000000000000011000000001101000000100", "00000000000100000000000000010000100000010100000001", "00000000000010000000000000010010000001000000000000", "00000000000010000000000001010101100000000000001100", "00000000000001000000000000110100010000100100010010", "00000000000001000000000000000010100010001000010101", "00000000000000100000000001000110001000010000000001", "00000000000000100000000000001000000000011000000000", "00000000000000010000000000001010100000000000100000", "00000000000000010000000000000000000010000100000000", "00000000000000001000000000001010000000000000000001", "00000000000000001000000000010000001000000000000000", "00000000000000000100000000000001100010010001010001", "00000000000000000100000000000100100000001010010000", "00000000000000000010000000000100000001000000000000", "00000000000000000010000000010010010100001000000000", "00000000000000000001000000000000000000100000010100", "00000000000000000001000000100100010110001100000001", "00000000000000000000100000010000010000000000110010", "00000000000000000000100000011000000000001100110100", "00000000000000000000010000000001001000000000100011", "00000000000000000000010000000001010101010010100000", "00000000000000000000001000000111100000000000100010", "00000000000000000000001000000000010010010000010100", "00000000000000000000000100000001000000010000000100", "00000000000000000000000100000100000100000100001000", "00000000000000000000000010000000000001000000001100", "00000000000000000000000010000000000000000000010001"}

Returns: "11111111111111111111111111000100100000000000000000"
50

50

{"00000000000001000000000000000000000000000000000000", "10000000000000000000000010000001000000000010000000", "00001000000000000000000100000000000000000000000000", "00000000000000100000000100000000000000000000000000", "00000000000000010000000010000000000000100000000011", "01000000000000000011000000000000100000000001000000", "00000000100000000001000001000000010000000000000001", "00000000100000000011000000000000000000000000000001", "00000000000001000001000000100000000000000000110000", "10000000000000000000000001010000000000010000001000", "00000000000100000000000100000000001000000100000001", "00000000001000000000000101000100010000010000000010", "00000000000010000000000010000000100000001000000000", "00000000100000000000110000000100000100000000000000", "00000000000100000000001110000000000000010000000000", "01000000000000000000000101000010000110000000000001", "00000100000000000000001000000000000000000000001000", "00100000000000000000000000000000000000000000001000", "10000000000000000000000000000010001000000100000000", "00000001000000000000000000000000010000000000000000", "00010000000000000000000000000000000000000000000000", "00000000010000000000100110000000000000000000000000", "00000000000000100000000000000000100000000001000000", "00000000000000001000000100000000100000001000000000", "00000000001000000000000010001000000000010000000001", "00000000000000010000001000000000010000000000000000", "00010000000000000000010000000000000010100000000010", "00001000000000000000101000000000000000010000001000", "00000000000000001001000000000000000000000000000000", "00100000000000000000000000000000100000000000000000", "00000000010000000000000000110000000000000000001000", "00000000000010000000000001000000100010000000000000", "00000000000100000000000000000000000000010000000010", "00010000000000000000000000000000000000001000000010", "00000001000000000000100000000000000000000010000000", "00000100000000000000000000100000000000001000000011", "00000000000000010000100000000010000001000000100100", "00000000000000100000000000010000000000000000000000", "00000000000010000010000000001000100000111000000000", "00000010000000000000000000000000010000010000000000", "00100000000000000000000000000000100000000000010001", "00000010000000000000000010000100000000100000000000", "01000000000000000000000100000000000000000000001000", "00000100000000000000000000000000000001000000001000", "00000000010000000010000000000000110000100000000100", "00000000001000000000000000000000000001000000000000", "00001000000000000000000001001000000100000000000100", "00000001000000000000001001000000100011000000000010", "00000000000001000000000011010000000000100100000000", "00000010000000000000000000000000100000000001000101"}

Returns: "11111111111111111011111111111110001001110101011000"
50

50

{"10000000000000000000000000001100010000000000000000", "01000000000000000001000011000100001000100000000000", "00100010000000000010000000000010000000000000000000", "00010000000000000000010000000000010000010000000000", "00001000000001000000000000000000000100000000000000", "00000100000000100000000000010001100000000001000000", "00000010000000000010000001000000000010100000010100", "00000001000000000010000011000000100000010000100010", "00000000100100000001000000000100001010000000000000", "00000000010010000000000000000000000000000000001010", "00000000001000100000001000000001010000000100000000", "00000000000100000001000010000000000000001000000000", "00000000000010000000000001000000010000000001000010", "00000000000001000000000100010010000110000000000001", "00000000000000100000000000000000000100100100000000", "00000000000000010000001100000001010000000000001000", "00000000000000001000010000000010000000100000000000", "00000000000000000101000000000100001000000000000000", "00000000000000000010000000001000000001000000010010", "00000000000000000001000101000001000000000100000000", "00000000000000000000100000000000100000000000000000", "00000000000000000000010000010101000001000000010000", "00000000000000000000001000000000000100000000000000", "00000000000000000000000110000000000000100000000001", "00000000000000000000000010000000000000000000001000", "00000000000000000000000001000000000000000001000001", "00000000000000000000000000100000000100000000001000", "00000000000000000000000000010000000000000000000000", "00000000000000000000000000001000000000000011000000", "00000000000000000000000000000100100000000000010000", "00000000000000000000000000000010000000000000100001", "00000000000000000000000000000001001000000000000000", "00000000000000000000000000000000100000000000000000", "00000000000000000000000000000000010000000010000000", "00000000000000000000000000000000001000000000000000", "00000000000000000000000000000000000110000000000000", "00000000000000000000000000000000000010000000000000", "00000000000000000000000000000000000001000000110000", "00000000000000000000000000000000000000100000000000", "00000000000000000000000000000000000000010001010000", "00000000000000000000000000000000000000001000100000", "00000000000000000000000000000000000000000110010000", "00000000000000000000000000000000000000000010000000", "00000000000000000000000000000000000000000001100010", "00000000000000000000000000000000000000000000100001", "00000000000000000000000000000000000000000000010000", "00000000000000000000000000000000000000000000001000", "00000000000000000000000000000000000000000000000100", "00000000000000000000000000000000000000000000000010", "00000000000000000000000000000000000000000000000001"}

Returns: "11111111111111011100100100111000000011001111010101"
50

50

{"00101010101010101010101110101010101001000000000000", "00101010101011101010101010101010101000000000000000", "00101010101010101010111010101010101011000000000000", "00101010101010111010101010101010101001000000010000", "00101011101010101010101010101010101000000000000000", "00101010101010111010101010101010101000000110001000", "00101010101110101010101010101010101000000000000000", "00101010101010101010101011101010101000000000000000", "10101010101010101010101010101010101000000000000111", "00101010101010101010101010101110101000000000100000", "00101010101010101011101010101010101000000000001000", "00101110101010101010101010101010101000000000000000", "00111010101010101010101010101010101001000000100000", "00111010101010101010101010101010101000000000000000", "00101010101010101110101010101010101000001000100000", "00101010101010101010101010101011101000000000100000", "00101000101010101010101010101110101001100000001000", "00101010101110101010101010101010101000000100000000", "00101010101011101010101000101010101000000000000000", "00101011101010101010101010101010101000000000000000", "00101010101010101011101010111010101000001000000000", "00101010101110101010101010101010101010100000001000", "00101010101010101010101010101011101000001000000000", "00101010101010101010101010101010101100000010000000", "00101011101010101010101010101011101010000000010010", "00101010101010101010101010101010111100001000000000", "01101010101010101010101010101010101000000000100000", "00111010101010101010101010101010101001000000000010", "01101010101010101010101110101010101000000100110000", "00101010101010101010101110101010101000110000000000", "00101010101010101011101010101010101000010000001000", "00101010101010101011101010101110101000000100000000", "00101010101010101010111010101010101001000000000000", "00101010111010101010101010101010101000000000000000", "00101010101010101010111010101010101000000001000100", "10101010101010101010101010101010101000000000001000", "00101010101011101010101010101010101000000000000000", "10101010111010101010101010101010101000000000001000", "00101010101010101010101011101010101010100000000000", "00101010101010101110101010101010101000000000010000", "01101010101010101010101010101010101000000000000001", "00101110101010101010101010101010101000000010000000", "00101010111010101010101010101010101000000001000000", "00101110101010101010101010101010101000000000000000", "10101010101010101010101010101010101000000000000010", "00101010101010101010101010111010101010100100010000", "00101010101010101010101011101010101000000100010000", "00101010101010111010101010101010101010010000010000", "00101010101010101010101010101010101000010001000000", "00101010101010101110101010101010101001010000000000"}

Returns: "11010101010101010101010101010101010111111011001111"
50

50

{"00000000000000000000000000001111111111111111100000", "00001111111111111111100000000000000000000000000000", "00000000000000000000111111111000000000000000000000", "00000000001111111111111111111100000000000000000000", "00000000000000000000000000000000111111111111111110", "00000000000000000111100000000000000000000000000000", "00000000000000000000000000000000000011111000000000", "00111111111111111111100000000000000000000000000000", "00001111110000000000000000000000000000000000000000", "00000000000111111111111111111111111111111110000000", "00000000000001000000000000000000000000000000000000", "00000000111111111110000000000000000000000000000000", "00000001111111111000000000000000000000000000000000", "00000000000000000000011111110000000000000000000000", "01111000000000000000000000000000000000000000000000", "00000000000000000000011111111111111111111111111111", "00000000000000000000000000000000111100000000000000", "00000000000011111111111111111111111111111111100000", "00000000000000000000000000000001100000000000000000", "00000000000000000000000000001111111000000000000000", "00000000000000000000000011100000000000000000000000", "00000000111111111111110000000000000000000000000000", "01111111111111000000000000000000000000000000000000", "00000000000000000000000111111111111111111111100000", "00011111111111111111111111111111111111111000000000", "00000000001111111111111111111111111111111111111100", "00000000000000111111111111111111111100000000000000", "00000111111111000000000000000000000000000000000000", "00000000000000000000000111111111111111111111111100", "00000000000000000000000000000001111111110000000000", "00000000000000000000000000000011111111110000000000", "11111111111110000000000000000000000000000000000000", "00000000000000000000000000000000000111110000000000", "00000000000000000000000000000000000000000000000100", "00000000000000000000000000001111111111111111111110", "00000000000000000000000000000000001111111111111100", "00011111111111111111111111111111111111111110000000", "00000011111111100000000000000000000000000000000000", "01111111111111111111111111100000000000000000000000", "00000000011111111111111111100000000000000000000000", "00000000000000001111111111100000000000000000000000", "00000001111111111111110000000000000000000000000000", "11111111111111000000000000000000000000000000000000", "01111111111111111111111111111111110000000000000000", "00000000000000000000000000000001111111111111111100", "00000111111111111000000000000000000000000000000000", "00000000000000001111111111110000000000000000000000", "00000000000000000000001111111111000000000000000000", "00000000000000000000000000000000001111111100000000", "00000000000111111111111111111111111111000000000000"}

Returns: "11111111111111111111111111111111111111111000000100"
50

50

{"10000000000000000000110000011010001000001000000101", "10000000000000000000000100000010100010100000000100", "10000000000000000000001000010000000000101010000101", "10000000000000000000000110000011000010000011000000", "01000000000000000000011000010110000000000000100000", "01000000000000000000001000000010000010001001000100", "01000000000000000000110001000000000000001000000000", "00100000000000000000001100000001000000000000000000", "00100000000000000000000011110000000000100001001001", "00010000000000000000000000001000000000000010000001", "00001000000000000000000000000100000010010111010010", "00001000000000000000000000010000000011000000101100", "00001000000000000000010001000100000000000100010000", "00001000000000000000000010001000001000100000000100", "00000100000000000000000000100000000100010001000000", "00000100000000000000001000010000000010000001000010", "00000100000000000000100100000001000000000000010010", "00000010000000000000001000011000000001000000100000", "00000010000000000000000100000000100010000010000101", "00000001000000000000011000001001001000100010000100", "00000000100000000000001000000000000101000000000000", "00000000100000000000100100000001100110110001000000", "00000000100000000000000100000010000000000000011000", "00000000100000000000100100101010000001001000000000", "00000000010000000000000100000101000000000001000001", "00000000010000000000001000010000010010010000000000", "00000000010000000000000000000010010000000010000001", "00000000001000000000000011010000000001000000000000", "00000000001000000000000101101001000001100101000011", "00000000000100000000010000100000010000000000000100", "00000000000010000000010010000000100001000101000000", "00000000000010000000100100000000000000010000111000", "00000000000010000000000000000100000000000001010000", "00000000000010000000000100001010000100000010110000", "00000000000001000000000011000100010001000000000010", "00000000000001000000110000000000000000000100010000", "00000000000001000000000000101010100010001000000100", "00000000000000100000000010010001000000010110000100", "00000000000000100000010010000000000100000101000001", "00000000000000010000110000000001000000000000100001", "00000000000000001000100000010000000001000000000011", "00000000000000001000001000000110000000000000000000", "00000000000000001000101000100000000000000000000001", "00000000000000001000101100000100100000000000010000", "00000000000000000100000010010000000010000100000011", "00000000000000000100100100101000000000000000011100", "00000000000000000100010000000010011001010001100001", "00000000000000000010001000000000000000000000001010", "00000000000000000010000000100100100000000000001010", "00000000000000000001100001000101100000011000010011"}

Returns: "11111111111111111111001000000010011100000000100000"
50

50

{"10111111111111111100000000000000000000000000001100", "01111111111111111101000000000000000010000000000000", "00100000100001100010000100010000000000000000010000", "00100000001000000000001000000000000000000000000000", "00100000000000001000000000001000001000000000000000", "00010000000010000000000000000000001000000000000000", "00010110100000000100000000000010001100000000001000", "00010000000000000000000001000000100000000001010000", "00001001010000000000000000000010000011000000100000", "00001010000100010000000000001000000010000000001000", "00001010100000000000000000000000001000000000000000", "00000100000000000000000010100000000000000010000000", "00000110000000010100000001000000000000000000010000", "00000100010000100000000000000010000000000000000000", "00000011000000000000001000000010000000001000010000", "00000010000000000000000000010001001000011000000000", "00000010001000100000000000000000000000000000001001", "00000001001000000001000000000000000000000110000000", "00000001101000000000000100000000000000000000000010", "00000001000000010000000100000000000000000000000000", "00000000100001000000000100001000000000000000000000", "00000000100110000000000000000001000000001000000010", "00000000101000010000000000000000000101000001000000", "00000000010001000000000001100000000000000000000000", "00000000010000100000000000000000000000000000000000", "00000000010000000001010100000100000001000000000000", "00000000001000100000000000000000000000100000000000", "00000000001000000001000000000000000100100000000000", "00000000001001000000000010000000000001000000010000", "00000000000100000000000000000000010001000000000000", "00000000000100000000000000000000000000000010000010", "00000000000100000000100000000000000001000000001000", "00000000000010000000100010000000000000001000000000", "00000000000010000000000000000000000000100100000000", "00000000000010000000000000001000000000000011000000", "00000000000001000000000000000000000000000000001000", "00000000000001000000000100000000000000000000000110", "00000000000001000000000000000000000010000100001000", "00000000000000100000100000100010010000000100000000", "00000000000000100000000010000001000000000000000000", "00000000000000100100000000000000000000000000000000", "00000000000000010010000000001000000100000000010000", "00000000000000010000000000000100000100001000000000", "00000000000000011000000000000000000001000100000000", "00000000000000001000000010000001000000100000000000", "00000000000000001000000000100000000000101110000000", "00000000000000001000001000000000000000100000000011", "00000000000000000101000000000000100000000000000011", "00000000000000000100000000000011000000000000001000", "00000000000000000111001111000000000000000000000010"}

Returns: "11000000000000000011101111111111111111101011001110"
50

50

{"10111111111111111111111111110000000000000000000000", "01111111111111111111111111110000001100010000000000", "00100000010000000000000000001000011000100001000100", "00100000000000000010000000000010000000000010000000", "00010000000000000000000000000000000001000000000001", "00010000010000000000000000000000010000000000000000", "00001000001000000000000000011010000000010000000000", "00001001000110000000000100000000000000000000000010", "00000100000100000000001010000001010000000000000000", "00000100001000001100000010000001000010001000000000", "00000010001000000010000000001000010100000000000000", "00000010000000000010000000000000000000000000000000", "00000001001010000000000000001000000010000000010100", "00000001000001000000000000000000010000000100001000", "00000000100000000000010000000000000000000100000000", "00000000100000010000000100000000010000100000000000", "00000000010000000000000100010010000110000000000001", "00000000010001000000000000000000000000000000010010", "00000000001010000000010000000000000000000001100000", "00000000001001010000000000001000000000000000000000", "00000000000100010000000010000000100000000000000000", "00000000000100000000000001000000000100001000000000", "00000000000010000000000000011000000000000000000100", "00000000000010000001000000010010000100000000000000", "00000000000001000001010000010000000001000000000001", "00000000000001100000000000000000000000000010000000", "00000000000000100000000000000000000000000000000000", "00000000000000100101010000010000000100000000000000", "00000000000000010100000000000000000000000100000000", "00000000000000010000000000010000000000000001001000", "00000000000000001000000000010000000000100000000000", "00000000000000001010000000100000000000000000000000", "00000000000000000100100010000000000000000000000000", "00000000000000000100000000000000000100000100000000", "00000000000000000010100000000000000001000000001000", "00000000000000000010000000100010000000000000001000", "00000000000000000001000000000000000000000000000000", "00000000000000000001010010000000000000000000000010", "00000000000000000000100000000000011000000000000000", "00000000000000000000100000000000000000000000100000", "00000000000000000000010000000100000000000000000000", "00000000000000000000010001100000000000000000000000", "00000000000000000000001100001000010000000010000010", "00000000000000000000001001001000000010000000000000", "00000000000000000000000100001000000100000000000000", "00000000000000000000000100000010000000000000000000", "00000000000000000000000010000000000000001000000000", "00000000000000000000000011000000100000000010000000", "00000000000000000000000001000000000010000010000100", "00000000000000000000000001000000010000000000000000"}

Returns: "11000000000000000000000000001111111111111111111111"
50

50

{"11111111111111111111111111000000000000000000000000", "11111111111100100000000011111111111100000000000011", "11111110000011111100000011111100000011111100000011", "11100011100011100011100011100011100011100011100011", "10101010101010101010101010111010101010101010101010", "10100000000000000000000000000000000000000100000001", "00000000000000000000000000000010000000000000000000", "00000000010000000001000000001001000000000000001000", "00000000000010000000000100000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000100000000001000000000", "00000010000000001000000000000000000000000000000000", "01010000000000100000000100000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000010000000000000000000000001", "00001000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00000000000000000000000011000000010000000000000000", "00101000000001000000010000000000000000010000000011", "00000000000000000000010000000010000000000000000010", "00000000100000100000000000000001000001000010000000", "00100000000000100000100000000000000000000000000000", "00000000000000000000000000000000000000000001000000", "00000000000000000000010000000000000000000000000000", "00000000000001000010000000000001000000000000000000", "00000000000000000000000000000000011000000000000000", "10000000000000000000001000000000100000000100000000", "00000000100000000100000000000100000000000000000000", "00001000000000000000000000000000000000000000010000", "00000000000000000000010100000000000000000000001010", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00100000000000000000000000000000000000000000000000", "00000000000010000000100000001000001010000000001000", "00000000000000100000100000000000000011100000000000", "00000000000000000001000001000000000000000000010001", "00000000000000000000000000000000000000000000010010", "00000000000010000000000000000000000001000000011001", "00000000000000000000001000000000000000000000000000", "00000000000000100000000000100000000000000000000000", "00000000000000000000000000000100000001000000000000", "00010000010000000000000000000000000000000000001101", "00000000000100000000000000000000100000000000000001", "00000000000000100000000000000000000000000000000000", "01000000000000000100000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000100100000000000000000000000010000000000000", "00000000010000000000000000110000000000000000000000", "00000000000000100000000000000000000000000000000000"}

Returns: "11111111111111111111111111000110011001000001010010"
50

50

{"00101010101010111010101010101010101010010000010000", "00101010101010101010101110101010101000110000000000", "00101010101010101011101010101010101000010000001000", "00101010101010101010101010101010101100000010000000", "00101010101011101010101010101010101000000000000000", "00101010101010101110101010101010101000000000010000", "00101010101110101010101010101010101010100000001000", "00101110101010101010101010101010101000000000000000", "00101010101110101010101010101010101000000000000000", "00101010101110101010101010101010101000000100000000", "00101010101010101010101110101010101000010001000000", "00101010101010101010101010101010111100001000000000", "00101010111010101010101010101010101000000000001000", "00101010111010101010101010101010101000000000000000", "00101010101010101010101011101010101000000000000000", "00101010101011101010101010101010101000000000000000", "00101010101010101010101010101011101000000000100000", "00101010101010101010101010111010101000001000000000", "01101010101010101010101010101010101000000000100000", "00101010101010101010101010101110101000000000100000", "00101010101010101010101011101010101000000100010000", "00101010101010101011101010101010101000000100000000", "00101010101010101010101110101010101001000000000000", "00101011101010101010101010101010101000000000000000", "00101010101010101011101010101010101000000000001000", "00101010101011101010101010101010101000000000000000", "00111010101010101010101010101010101001000000100000", "00111010101010101010101010101010101000000000000000", "10101010101010101010101010101010101000000000000111", "00101010101010101110101010101010101001010000000000", "10101010101010101010101010101010101000000000000010", "10101010101010101010101010101010101000000000001000", "00101010101010101110101010101010101000001000100000", "00101010101010101010101010101011101000001000000000", "00101010101010111010101010101010101000000110000000", "01101010101010101010101010101010101000000000000001", "00101010101010111010101010101010101001000000010000", "00101010101010101010111010101010101000000001000100", "00101110101010101010101010101010101000000010000000", "00101010101010101010101010101110101001100000001000", "00111010101010101010101010101010101000000000000010", "00101010101010101010111010101010101001000000000000", "00101010101010101010101011101010101010100000000000", "00101110101010101010101010101010101000000000000000", "00101010101010101010101010111010101010100100010000", "00101011101010101010101010101010101010000000010010", "00101010101010101010111010101010101011000000000000", "00101010111010101010101010101010101000000001000000", "00101011101010101010101010101010101000000000000000", "01101010101010101010101010101010101000000100110000"}

Returns: "11010101010101010101010101010101010111111110001111"
50

50

{"10000000000000000000000000000011000010010000000100", "01000000000000000000000010010100100001000000010100", "01000000000000000000000010000010011000000000000000", "00100000000000000000000001000100100010000000001010", "00100000000000000000000000000000101000110010010000", "00100000000000000000000010000100000000000000010000", "00010000000000000000000000000100000010101000100000", "00001000000000000000000000000001001100100100001000", "00001000000000000000000000111100000000100000001010", "00000100000000000000000000000100000000000100000000", "00000100000000000000000001111000100000100010000011", "00000100000000000000000000000010001000011101110000", "00000010000000000000000000100000010000000000100001", "00000001000000000000000010011000010000000010100000", "00000001000000000000000000000000000000000101000001", "00000000100000000000000001000010000000001001000100", "00000000100000000000000001011000100000000000010000", "00000000100000000000000000110001001100001000010000", "00000000010000000000000000000000100011100110010100", "00000000001000000000000000000010101010000101110000", "00000000001000000000000001000000010010000100000000", "00000000000100000000000000001101001100000000000010", "00000000000100000000000000001000000100110000100100", "00000000000100000000000000000100011010000010000000", "00000000000010000000000000100100000010000000000010", "00000000000001000000000000010000100000001000001000", "00000000000001000000000001000111000000010011000001", "00000000000000100000000000011100110001000001010000", "00000000000000100000000000000000000001010011000100", "00000000000000100000000000011010000000000000000000", "00000000000000010000000001000000001000011000101000", "00000000000000001000000001101001000000000000000000", "00000000000000001000000000000000000000010000110101", "00000000000000000100000000000000000000000000000010", "00000000000000000100000001000100001101000100000000", "00000000000000000100000010000010100001001001110000", "00000000000000000010000010100111101010100001011001", "00000000000000000001000000010010000000000011011000", "00000000000000000001000000100000000100000000100000", "00000000000000000000100001100010000000000100101000", "00000000000000000000100001000000010100000000000000", "00000000000000000000100000010000010000000010000100", "00000000000000000000010010000110010000010000000000", "00000000000000000000001001000001001000001000000100", "00000000000000000000001000010000100010000100000000", "00000000000000000000000100100101001110000000000000", "00000000000000000000000100000010000000100010101010", "00000000000000000000000100000100011001100000101001", "00000100000100011000001010001000100110000000110110", "00000000000000010001010100000101010000010100000010"}

Returns: "11111111111111111111111101001000000101000000000000"
10

20

{"00010111011100101010", "11110001010110011110", "00101010100100000100", "11000000111011101000", "01100101011001100100", "11010010110010000100", "01111111011000010001", "00001010111010011111", "11100011101000011011", "10001000011001001111" }

Returns: "11111101000011000110"

Statistics

Problem Statement for "EllysLightbulbs"

Problem Statement

Definition

Constraints

Examples