TopCoder Statistics - Problem Statement

Problem Statement

This problem has a non-standard time limit: 4 seconds.

There are lots of tasks about lamps and buttons. Today you have to solve another one.

We have m lamps, numbered 0 through m-1. You are given a String init with m characters. The String init describes the initial state of the lamps. If the i-th (0-based) character of init is '1', lamp i is initially turned on. Otherwise, the i-th character of init is '0' which means that lamp i is initially turned off.

In addition to the m lamps there are n buttons, numbered 0 through n-1. Each button is connected to some subset of lamps (possibly none or all of them). You are given the information about the buttons in the String[] buttons. For each i and j, buttons[i][j] is '1' if button i is connected to lamp j, or '0' if they aren't connected.

Pushing a button toggles all lamps that are connected to the button. (I.e., the ones that were on are now off and vice versa.)

You already realized that the order in which you push the buttons does not matter. You also realized that it doesn't make sense to push the same button twice, because that has the same effect as not pushing it at all. Therefore, you have decided that you are going to push each button at most once. This means that there are 2^n ways to push the buttons. For each of those ways we are interested in the number of lamps that would be lit at the end.

Compute two values:

X = the largest possible number of lamps that will be turned on after you push some buttons
Y = the number of ways in which you can push some buttons so that in the final state exactly X lamps are turned on

Return the long[] {X, Y}. (That is, a long[] of length 2 in which element 0 is X and element 1 is Y.)

Definition

Class:: BrightLampsRemake
Method:: maxAndCount
Parameters:: String, String[]
Returns:: long[]
Method signature:: long[] maxAndCount(String init, String[] buttons)
(be sure your method is public)

Constraints

n will be between 1 and 50, inclusive.
m will be between 1 and 50, inclusive.
init will contain exactly m characters.
buttons will contain exactly n elements.
Each element in buttons will contain exactly m characters.
Each character in init will be '0' or '1'.
Each character in buttons will be '0' or '1'.

Examples

"0000"

{"1010", "0100", "0001"}

Returns: {4, 1 }

In the beginning all lamps are off. You can turn them all on by pushing each button once. Thus, it is possible to have X = 4 lamps on. The above way is the only way to achieve this number of lit lamps, hence Y = 1.
"1011"

{"0000", "0000", "0000"}

Returns: {3, 8 }

In the beginning three of the four lamps are turned on. There are three buttons. The buttons don't do anything. Thus, we have X = 3, and each of the Y = 2^3 = 8 ways of pushing the buttons leads to a state in which three lamps are on.
"00000"

{"11000", "01100", "00110", "00011", "10001"}

Returns: {4, 10 }
"10000"

{"11000", "01100", "00110", "00011", "10001"}

Returns: {5, 2 }
"0"

{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0", "0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

Returns: {0, 1125899906842624 }

Watch for overflow.
"0101101100101011111111100000011000110111111000"

{"0000010011000000011000111101001101110100110010","1001010101000101101101010000111001111111010011","1000101000111011111111101111011000111110111001","0100101100011110001000110001000011110011111101","1001001010111101110011001110000101101101100010","0001010010101000001011011111111111101001110000","1000011010101110111000000001100001101010001110","1001010010110110111110100110110100000001100101","1010111001110111011101011011111000101011000110","1000001000001010100010000011110101111001101000","0110001011010111111111110001101111100010010110","1100011101011001101001111001011011111000111111","1001111011000101011011100010000110001110011011","1100010110010111001001010011011111010000000100","1011100001100001100011010010100110000001000000","1011011010111101000000010010100000111011111010","0010001111011111101001100011010001110011001001","1000001110001000001101101000111110000100010011","1011010010001001001011110111101001111101000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000"}

Returns: {38, 16 }
"101010110001011100001101010"

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Returns: {27, 524288 }
"00101111001001010000100111010010100110001111100001"

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Returns: {44, 4096 }
"01011000111111101011100111110100100101011101000"

{"01110010010111110011010110101010110100001110110","10100011000110100010011011110010000010101110000","00100100011011110010101110010000000101110010000","00010010000110001000000010100101000011111110110","10010010011111001000001000111111111010100000010","00010101011110110100001110101110001101010000001","00011110100111101000101101010101110011110001011","11011100001001011101111101011011000001011011000","01010101001100100101000110001010000111011010101","10111011100111000111011101110001011111001010000","00100101110010100010111000100111100100101100001","11111000110010011110101001100100101110100100001","11110000100111101000110000110010100101001101100","11100001010001110000000100111001101001100100101","11111000111010001010011101011011100001001111011","11000111000110011101100011010100111100110010010","01110011100110110001001111111010011001000001100","00010101000101100001000100110001000011001011011","11100101110101110111001100101001101001111101100","10100110011111101101111000010100011001001011000","10011000011000011000100101101111100010100000100","01000010111101000100001001101100100100101111010","10100110011100010001100000001111010110100001011","10101001011101101000101000101001011111100000100","11101000000111101111110011111010011110001001000","11011110110101100001001001001001000110110001000","11010000011011000000101001011000010100110101110","11001001111000111110001001000010010100101001110","11010000110010011101001011010101001011100011111","00011101111001111100111001010101010011101110101","00101111010110111100011110001110111001000110111","11001011111101111111110101000010000111010010011","00001110101100100010111111010001101110100001110","01111101010100001110001110001011110111111000110","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000"}

Returns: {44, 4 }
"001000011101110100001100101001101010111011001"

{"111100110111111100100110011110000101110001110","001010101001010100111101010001110101101011110","101100001011111001110010110111101000011101010","001011001111000010010100111000001011101101101","000011011011011001100011001010101001000101100","011010000000001100110100111110010010001111101","111111111011101010101101101101010111100000011","011010111001101011100101110110110101100010110","011100001001111010001011101111111100000011010","111000001001010001100101000110001100100010101","100101010110001101111101000110100100110110011","100101000101110011001111000101000010001011111","010010000011001010010010010111111011100001010","111101001001010000101000010100000001001000111","011100011101101011000111110001001011100000100","001010100010001000101000101001001011111100000","010000111111010001010011000101110110100001111","101111001110011110011110011110100011010111001","011110111111110111101000100000110000110000000","110011101100001000000011111100100010101010111","111110011001000101010110011100000010001001000","110001001101100010110111000001010110101010111","101010000111101101011110100000010110101100110","011011001100001010110101000111010101001110000","000100100111000010000011011111111010101010010","111011011000100011011000100001111100110101010","101110010010010100010000011110100001101110001","001000011011010011111100000100101101101001000","010110000001010101000010111100001000010100101","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000","000000000000000000000000000000000000000000000"}

Returns: {40, 3328 }
"00000000110100001001100101101100110010101001001"

{"11011101110011011011011111011010100110000101000","00010001110111101010001011010100111111011100001","00010000100110011111001011101100100100111100101","10000100101100110001110010000011011000111100001","10110111100111010010111100110111110011001011010","01000101111001100111100100001101110010001111111","00110111001111100101100101011001100001101000011","00000001101100101110010010000000000010100100010","01111100111000101111000001000100111010000000001","11001101000101000111100101001010111101100000110","00100001011110100000100001000110111001111010101","00110101001110011001100111111010111010111100010","00111100000110001000000100010001011000001011010","01011001010001011001101100001000000011111111001","00011000001001100000110011100000110001001111101","10000000101000100010100101011010001010101010010","01001000011100011010000111001101100000010010000","11011001111110100110001100010101100101110111101","11111010101001111011111100101001101110010000100","10001001000110100100010001101100100110000100001","00010100101000110100110000011001001100010000111","10111111111010001000001100000110011101100000000","01011000001100100101111101010011111001101100001","11000011010010110001100111001011100110110011011","01000011111110110011011110101001111011110001001","11110101101100011000001000111111011010110101100","01011101000101100111111100010110110001110110010","01001111101100010001000011100001101011011000010","10100101001000000011110110001011011001010001011","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000"}

Returns: {43, 2048 }
"00101110000011011010111011010101101010111000111111"

{"11010000110000110110101011101000011010110001111100","11010110000101000010100011010110010001001000000000","01100100011001101010001111101001110111001010011011","11011110010001010110100111111111100100111010100100","00101011011111110000110011010001000000000011001001","10100111101000101010011101000000101111000100000101","01101000000011101010110010011100011011010111011010","10011000010010001101100111101100110000111110011100","01100110100011011110010001000011110100010100100010","01011001011101001110111101001000010010111000010101","10100001010100000000011110110101010100000010110000","10011000001011101010000010100001010001001111010101","00011000111110001010100110100001011100000110101001","11101011100010100101001100000110001001011000111111","10101000111011110100110101110011000100100011101100","10011010001000011001010110001101100110011111001000","11111111000000001111111100111010110000011010010101","10001110010001101000010011110000101010000010010110","00101111010110110011001010000111000101111011100111","10110001101010111101010110111101110110001000100111","11010001111111101110101011001001100010011010001010","01000110010001100100111011010001110101011001010000","01111110110000101111001110000000110010011101010100","00111011011011111100101101101100011001111011000101","01010100100001110110010010011001001010111000010001","00010110010000011000101110110111101110011110111110","00111011011110010000111101000011111001111000111101","11000001101101011000010111110000100100011001101010","10010111001101100000000100110110001001001111100110","01100101101010100011110010010111111010101110100111","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000"}

Returns: {45, 131072 }
"0100010111010001001110010100110010110011101100000"

{"0000100000000010110101100000001110000110001001001","1101010010111011101011011110000101010001111101001","1100110010100110011101010111010110110001000100101","1100111100110111000100011110100001001011100001111","0101101010011011110010101100000111100100101110111","0011111111001000110001000000100101100110000001010","1111110010010011001001110101110001011000101100011","1011000011110100000111001011010111110101100101101","0111011011111011011000100100100001100111110011001","0011000110011000001100001101110011000001010000011","1100010010000001111000001011010100010011001001101","0100000100111000111100001000010111111101101101101","0110110111111010110111000000011111101000101011110","1011010100110101011110010111010010011100001111001","1011000111101000100110101111011000001000100100001","0011100100011010011000100011000110011100011001111","1001010110100100000100011001001001011010011010111","1010011111101011100110000111101011101011110011000","1000001100110000100100011101000111111110110000101","0010011000111100111111010101101110111010101100110","0110011101001000000011001010001101101001111111011","1101000101101010111100011001001001010000100001101","0000001100001001100111110101000111000110100001000","0010001110110110010001110011001110111010111110100","0010101011011010101010001110001010010100100010001","1100011110111110000000101000100101000010110001011","0000011010000110011011110010110110001110001011101","1110010101011100011100110011010100100010111101100","1100001010100100001100011101000010010000111000011","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000000"}

Returns: {43, 1835008 }
"01111010010010011110001110101000101010100011110010"

{"00001001010010001111011100100011010000110101110101","10011110000110110100110100111110011100010111100011","01101010010001101011000010101010101111110111110000","00010001100001101001001011010100010110010110010100","01011111010101010010000001010111101000011100101010","00101001100011110001110100111010101001011011100000","10101101000011011100011010101100110101011010110011","01011111011001001000101010111011110111110010101001","01000110000011111100010011011111001011100000100000","01110100010001011101011100000001000000111100101000","10011101011010010011010011111111011001001000000000","00111101111100111101010001100000010101011101101011","01111010011100010000001001111110010100111110111001","01000101101101001111000110100100011001101100101101","00111101100000100000001001000001100111111111010011","10001111000011100001101100010001011110110011001001","01001101101111100010111001110101000011000100000110","10000011000000101000000111100100101001011000000011","00101000010011011000011011011111000001111000100100","10111110110100010010001111000101000000111100000111","00001111001110011001110010100011100100010000011101","00001110110100110111001100010001111110001010000001","00101101101111001010110000110100011010000100100000","01110101111110111000000001000110011101111101111010","00101000101111011000001111111010100111010100110000","00010010011101101111001001110101100010000111000000","00110011011000110001001001110010111010010100100100","01001011001010001110001111101000001000000100100110","10010100010001011110001001001100010101101111001011","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000000"}

Returns: {46, 2048 }
"01010110101010001011110111101111001011010011001"

{"00001110110000010001010110111100101010111001100","01011100011011000001111000100010000111110000100","10000010110000000011011001001110100010001110111","11011010100101010011110001110000010111001011000","10010001001111010001001010010000111100011000100","01111010101111010110100011000001101110011001111","00011001010010111011001110010011001101100011111","10111001000001110010011100010000110101110011110","11001011011101110000001010000100100111100101001","10011101111110101011110011101011010000110110111","01010011100101010111001100101010001000101111001","11101100100010100010001010111010100110010110011","01111001000010100011101000000101011010001110110","00110111101111101101001010000111111011000111101","00101101110111100100100011011101100100000000000","10111100110000101011011011110011111111111100111","01111101110111000101100100111010000100010100001","11100100001111000110001010010110001011001011010","01010000010011111011110110011011111101101101101","10000100011100101000001000001111101000010011100","10110100100111001101111100110100011010000111011","10100011011000010110011001111010100001001010111","11001111010010010010011100111001001011100001101","00001010111000001110100010101101011000010110101","00010101000001111110001010001001101011011110100","01110111010100001110011000010011011110101001100","00110101010111111001110000000001111001101111110","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000","00000000000000000000000000000000000000000000000"}

Returns: {41, 11264 }
"00111011010100010010000110001011010111011111110110"

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Returns: {44, 8388608 }
"00111011100100000010010110011010111000100111110110"

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Returns: {44, 786432 }
"00111011111010010101100110101111101101001011010000"

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Returns: {45, 128 }
"00001110111111011101011111100011111000110100100000"

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Returns: {45, 524288 }
"10010001110001000011101101101010000001110110100011"

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Returns: {44, 196608 }
"0101101100101011111111100000011000110111111000"

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Returns: {38, 16 }
"1100010011110010"

{"1000101011001001","0000000000000000"}

Returns: {9, 2 }
"010111111100101110"

{"100111100111110101","110101101100001101","010011000010011000","000000111010110110","100000110110000100","100110100001010100"}

Returns: {15, 1 }
"101010110001011100001101010"

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Returns: {27, 524288 }
"00010100100001101010010010010101011011001000100011"

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Returns: {34, 1 }
"0010011110111110101000101010001010001"

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Returns: {32, 1310720 }
"100"

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Returns: {3, 1099511627776 }
"0111000000001011000100010111100101111010"

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Returns: {27, 64 }
"00001010"

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Returns: {8, 268435456 }
"0111010000101111111110110101110100111111"

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Returns: {27, 67108864 }
"01110101110001001100"

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Returns: {10, 274877906944 }
"01111111111"

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Returns: {10, 60129542144 }
"01110101101110110110"

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Returns: {13, 49152 }
"01011100101011011100111101100111010"

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Returns: {28, 201326592 }
"01111100100001110100111"

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Returns: {23, 8192 }
"00100"

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Returns: {4, 536870912 }
"11"

{"10","10"}

Returns: {2, 2 }
"000101001001011101101000111000101"

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Returns: {24, 20971520 }
"000110011000000"

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Returns: {9, 64 }
"00000000100100110110111111101100011100010"

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Returns: {29, 512 }
"00101111001001010000100111010010100110001111100001"

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Returns: {44, 4096 }
"00011001001000111011001010110011011100100101101010"

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Returns: {24, 1024 }
"111100001"

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Returns: {9, 256 }
"0110010001011001001111001010110001110100"

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Returns: {24, 549755813888 }
"101110101110001101101100011111111010010111110"

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Returns: {29, 1024 }
"11110111111000100000111011100101101011000010100101"

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Returns: {27, 16777216 }
"01011000111111101011100111110100100101011101000"

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Returns: {44, 4 }
"00110110101000000010011101100110000"

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Returns: {14, 8388608 }
"001111001111100000010011100110010"

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Returns: {20, 4398046511104 }
"100101001110"

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Returns: {11, 4194304 }
"001111000101101011"

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Returns: {13, 524288 }
"00010001010010101010100"

{"10001001110100111100110","01010001101111001111000","00000010100100000010010","00000000000000000000000","00000000000000000000000","00000000000000000000000","00000000000000000000000","00000000000000000000000","00000000000000000000000","00000000000000000000000","00000000000000000000000"}

Returns: {13, 256 }
"010001010010001111010001101101101001101101111"

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Returns: {28, 1 }
"0010110010110001001001011111000101111"

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Returns: {29, 34359738368 }
"0000000"

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Returns: {0, 549755813888 }
"110101010100101101001100"

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Returns: {15, 536870912 }
"10000100011111000011001001001101101001011001"

{"10111001100110010000101101101110011100100010","11110000110010010011100011011101101100000100","00101110100001011101110101001011100110111110","00101100001101100001110111000010100001001101"}

Returns: {27, 2 }
"1000010111111110010110110101101010011110011000"

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Returns: {38, 24576 }
"101010101010101110100000100011110101011111000011"

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Returns: {34, 512 }
"001011010000100111110000110000010100"

{"011010100110010101000111000011111001","001001101101000110001011110110000001","000101010111001010101011110001000000","010000011001000010101100100000011101","001100110100001100001000000111001100","111000000000011011001011011010001101","011101010001110110100001111111010010","100100001111001010100010010110000010","111101110100110110010000001101101010","110010000001000100010010110100110010","111111001110011110100000110011001000","100010100011001111011010010101111000","100100011011000010110001011001011111","001111111110010100010101100011111000","110011110010101111010110011111111110","011001000000101010101100001011011001","001101011101000101100100001000101001","010100111110111000111010010001110000","110000010110101001001010010000011110","011011001000001010001110000011100110","110110101010010010000100111100110101","110111010000001101001001011101001101","010001101000011010111000101110101100","111011011010101100101010101011001000","001001000100010010100011010100011100","110001110111011011011010101001000011","010001100110000100100011101101100101","100000001111100110000101000000011001","110000111011100111010011100111100010","100100110110110011101100000111011001","000010100000010001101100110100111111","110011001001011110101000110100011011","100000110000000001000011101111011010","010100001111001001011001100111110101","000110010110110110101100111110111100","100010110111011010111110100111110000","110010001011011111100111100111000000","000111111011110100001100100010110100","000000000000000000000000000000000000","000000000000000000000000000000000000","000000000000000000000000000000000000","000000000000000000000000000000000000"}

Returns: {36, 64 }
"1110001010111101101010010110101000110011"

{"0010001011011001111000000101100011011000","0001001101011101111010000101110011011010","1110101011100100000000101011111111000001","1101011110101101101011100111001101101010","0011100001111011011011001100011111100000","0010010011111010101011111111010111110111","0000101011000000001100110011010100100000","1011111110000010101011011001101011000100","1001001101110001011001000000001111110111","1100110110111101010010100100001110100111","1111011011010010101110001001010101100100","0010101011001110101110011100110110000101","0100001100110010001111100010100100001110","0001111100101011110100000001110100110001","0001111111001001110100110001011111101110","1001111101101011111000000010000001001000","0010010110110010000010000100011011001110","0101001000101011100111111110100111110001","0011011100000101111100011110001001100010","0110101101100011111001010100111001100101","0110101010011001000011101010010000101010","0000111100100000000001001110000000000110","1000010000100010010100111100100101100010","0110101100100011000100000010000010010110","1101010001010101110000111010100001010000","1000001011101101000001110100011100111001","0101011011111011001111101101000100111100","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000","0000000000000000000000000000000000000000"}

Returns: {37, 128 }
"11110"

{"10100","01111","01010","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000","00000"}

Returns: {4, 13194139533312 }
"010110"

{"110101","100100","110100","000101","111011","001101","111101","000000","011101","000000","000000","000000","000000","000000","000000","000000","000000","000000","000000","000000","000000","000000"}

Returns: {6, 65536 }
"100111010001001001011100001111100"

{"000001110010001001101101001010011","101110001101000100101011001010011","111001110111010011101100111011001","101001111101010011000000110010100","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000"}

Returns: {21, 786432 }
"1"

{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

Returns: {1, 33554432 }
"0011000110010011101010001101000000101110110100"

{"1010001010111001001110111001100001101010010101","1110101011000101011100101010111111010110001111","0000000011111001101001111111000101001101110111","0110100101100111011001001101001011011100101101","1101000111111001111101101101011010011001111011","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000","0000000000000000000000000000000000000000000000"}

Returns: {32, 16777216 }
"1011010110110101100111110101"

{"1000010001001111011001010000","0000010111110100011110110000","0001101110101101111100000100","0110111001001011101101000000","1011100010110101011101000010","0101000110001111111101110001","1000010011001011110111001111","1101101000011111100010011001","0101010001000001100011011001","1110011011010111011000010001","1000111101010111101010100000","0000001000111110110011000101","0000000000000000000000000000"}

Returns: {23, 2 }
"10110"

{"11110","00111","00010","11110","10111","00010","01011","00111","11000","01010","00000"}

Returns: {5, 64 }
"101110101000100111001110000011111000101001"

{"100010101000101110110001000001010000111111","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000","000000000000000000000000000000000000000000"}

Returns: {21, 140737488355328 }
"1100101"

{"0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000","0000000"}

Returns: {4, 33554432 }
"0101101100101011111111100000011000110111111000"

{"1110011111100100100100110000000001001101001011","0010101000011101100111111001110001001010101110","0110111001000001101100000110000111101100000000","1000100101011111110011000000111110101101000010","1100101110110110001110001100000100001001100111","0111101100111000010010011111101010010001010111","0000010111000101101010001000001100010010011110","0101010101011010110110000010001100010110101110","0001110001000010000001100001001111000000001110","1110001101001111110111001001101010011111101000","1101011001010111001011110101111111011001000011","0011100110111011011101001111100000011001101011","0100000100100000000010010010111000111010011011","0000100100000100101000100010001001000000100101","0000110110000100100010011000000100111110000010","1111010101101010000011111000110001010011110110","0000101100001111111101111110101111000100001010","0010111101010010100011111011100000111111110100","1100110000011000111111000000011001000010000100","1110001011011101001101110010101101100100010010","0001100101001011100110111011000010110111100110","1101101000011001011100011110000001101100101100","1111100011110111000010100000000100010010001001"}

Returns: {38, 16 }
"000010010101011000"

{"000000000000000000","000000000000000000","000101000110110011","000000000000000000","000000000000000000","000000000000000000","000101000110110011"}

Returns: {10, 64 }
"10000101010110101011000000010000101111100"

{"00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000","00000000000000000000000000000000000000000","01001000000000011011111100001011100101011","00000000000000000000000000000000000000000"}

Returns: {23, 274877906944 }
"1000010000100100110001101110110011111011011111"

{"1111010110001010001110011010001110111111010101","1010111100011100010100011110100111000001010101","0000101011111011000110001011010000011010000110","1110011011111110000101111100110001001111010011","0011000100101100100111101100011101110100010000","0111010000011001010000001100000110101110110011","1000010010000100010100010110110110100101010101","0001100011000001101110010100001011110111001101","1111110110000101100100000101010010010010011101","0011010011000010001001110101001110101110011101","0000000000100100100110111011000100100110111010","0111011110000101010110100001011100000100101010","1001111010101101111100110110000101100100110110","0101010010111011010000000000101011110011100000","1000011000101111011110101001110111100011010111","0101100011110111001111101111101101101111000010","0101110111101111011000111011010001100110000010","1110010100110110000100010101110110000101110100","1110110100010100100100101100001101001101110010","1110011101010110101011111111000100001000100011","1100101010100111010001010111001010111001011010","0101001110011010101011000110110111000010100011","1001011101010110101010101010101000011100101011","0001101000011011111001010101101101111000111100","1101110011000000101000011110010111111001001001","0010100010011100111001101001101101101010011000"}

Returns: {42, 2 }
"1111011110101001000010100001001101101011111111001"

{"1010101000111000111011000110111100001101111010110","0010111011101011101010111101010010111000011100010","1000010100111111000011101111101100001100101101100","1010011000000010110001110011101101110111100001110","1010101100111010100001101010000100101001100100111","0011010101000100000100101010111101100011101000100","0000000100000010011010101100111000100100011110001","1001001110101000111101100001101010001001011100011","1010101011010110110011111110000110010000101111111","1000010111010001001011010111010110010001111000101","0010001000111111101000110000111001011111010010011","0010001000111111101000110000111001011111010010011","0001101010101101110100111011010111111111101010111","0010111000000101100010000101101000100101001001011","1001111010010000101101111000000011010111011001010","0000110011010100000010001101101011100111001110001","1000100100000101001001011010111101110110110110100","1001111001111110100101000000111001001010001100011","0001101010101101110100111011010111111111101010111","1001111110010010110111010100111011110011000111011"}

Returns: {34, 16384 }
"010010010111100100100111111010000"

{"000000000000000000000000000000000","000000000000000000000000000000000","000000000000000000000000000000000"}

Returns: {16, 8 }
"100111000111110010110001001111110110100100"

{"000000000110101111110011011011110011101111","010011011010101100101101001011100111000001","011100010001111111101111101001110110000100","011101100100010000111010000101110101011000","111010111011101110101010011000011010111000","111110001011100000000010011111001010111101","001101010001110001101110111011000111111000","011010110010101001100100011011111011010111","110100001100101000110010111010000011001010","011111110010011010010100110101010100000110","100001111111010101100101110001101101010100","001101100111010010000010101101111101011101","110001000011001110111110100011010100011111","110011101001100000001101110111001011101000","100011100011011000111010110011001000000110","110100110000001100101111011110111101100011","001110110100111011100110111100010110010101","010100110101100011100011110100101011101111","111101101101010111110100000110010100110111","011001101000111010001111100110011011110100","110011101100110010000000110010110111100000"}

Returns: {30, 4096 }
"1011010111111000000010110000011"

{"0011010101001100001001100001010","0001101010001100111000111000011","0101111001101101011110010111000","1011111010010100111010100111100","1010100111110000111111001000100","0000101110010001101100110000001","1101111001100100101110100001111","1100110101101100011101010110001","1000100000101011111010000000111","1010001001011011011000110110011","1110100011111011001000110110000","1100100001110100010010011110100","0100001100110011100100101110110"}

Returns: {26, 1 }
"1111011111011110100011"

{"0011001001000101101100","1000110110100111111001","1000110110100111111001","0000000000000000000000","1000110110100111111001","0000000000000000000000","1011111111100010010101","0011001001000101101100","1011111111100010010101"}

Returns: {16, 128 }
"10"

{"00"}

Returns: {1, 2 }
"10101001100"

{"11001110101","00110110111","10111101100","10001011011","10111101100","01000110010","11111000010","01000110010","00000011100"}

Returns: {9, 32 }
"11111001010101001101000011011010001101011"

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Returns: {35, 2147483648 }
"01101100001111101111100"

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Returns: {20, 192 }
"010101010010101101000001011111111110110"

{"100000110001011111101001001000001101111","111011011101010111010011101011110101000","001111110101001101010110110001001010000","001101000111011101110101101001101101011","101011001111010001110110010010011101100","101101000000010010001001111100100100001","110001010000011011011111010111011010101","011101011001001110010110010101111111111"}

Returns: {28, 1 }
"010010000011111000101111000011010"

{"001110001110100011111111110101110","001101111011000111000000001000011","000011110101100100111111111101101","000000000000000000000000000000000","111110110100111000000000111011001","111110110100111000000000111011001","001101111011000111000000001000011"}

Returns: {23, 16 }
"0110000"

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Returns: {7, 2199023255552 }
"0110100110110010011101010101101000100101"

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Returns: {26, 2048 }
"0010100"

{"0000011","0010000","0110101","0010000","0001000","1100011","0000100","0010011","1101100","0000101","1110000","1001111","0000100","0010000","1100010","1010000","0010010","0010010","1011110","1101011","1100100","1010101","0101111","1101010","0111010","0011111","0110010","1110000","1000001","0000011","0100101","1101000","1110011","0001100","0100010","0010100"}

Returns: {7, 536870912 }
"0111001000001101"

{"0000000000000000","1000000010010000","0010001011101110","1010001001111110","1010001001111110","0000000000000000","1010001001111110","1000000010010000","0000000000000000","0000000000000000","1010001001111110","0010001011101110","1000000010010000","0000000000000000","0000000000000000","1010001001111110","1000000010010000","0000000000000000"}

Returns: {10, 65536 }
"1001110001011000110101111100"

{"0000000000000000000000000000","0000000000000000000000000000","0000000000000000000000000000","0000000000000000000000000000","0000000000000000000000000000","0000000000000000000000000000","0000000000000000000000000000"}

Returns: {15, 128 }
"00110011100010000011011101010"

{"11110011010010010001111010101","01111010100010101001101011001","10000010001000110010110010010","10101011011101100001101101100","11011111000100101110010111111","01011110100100110001110100100","00001011111000001010100011110","00101001010101010011011111110","11111101101001110111101011111","11011111000100101110010111111","10100000100101101011001110010","11011111000100101110010111111","11011111000100101110010111111","00100100000110011000011111101","10001010011000010101000000101","11111101101001110111101011111","01111100001001101000001000100","10100000100101101011001110010","01011101001100011100100101101","11011010000111000010100101011","11110101111001010000011001000","01010000011111010111100101110","01110100011001001111111010011","01111001001010000100111010000","01010101011100111011010111010","10101101110110100000001110001","00101010111101111110001110111","00100111101110110101001110100","11111000101010011011011001011","10000010001000110010110010010","11111011000010110110001000010","00001000010000100111110010111","11010111010100001001100101000","10100110001110101010101101111","10000010001000110010110010010","10000001100000011111100011011","00101100010110111111101101010","10000001100000011111100011011","10101000110101001100111100101","10101101110110100000001110001","01010101011100111011010111010","01111111100001000101011001101","01011000001111110000010111001","01111100001001101000001000100","00101010111101111110001110111","00000101000011101100110010100"}

Returns: {20, 2199023255552 }
"111110101010001111110"

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Returns: {17, 8796093022208 }
"0011110111001101011"

{"0110010100101001110","0011011011110100100","0010111111010100000","0010111101001000101","0110111011011110110","0010011111000111101","0110100001101010101","0100101111101100010","1011010000010011011","1010110101110000010","0010000110001111000","1110001010101101010","0110001011110001001","0000101111001101100","0010100100110011011","1000010111011010110","1010011010000000101","1011100011010100110","1111011100010111000","0001111100010101000","1100001010100101011","0011100011010110101","1110011110101010110","0100011010000110101","1011110000010111000","1010100110011110100"}

Returns: {18, 2560 }
"00101010001101000010001001"

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Returns: {26, 524288 }
"0111111111110000111011111000011"

{"0000011110000010000010110101011","1011001111011101001111001010101","0100111011111101100111111111010","0000010110100111101010010111110","1011111001001010011011011100100","1011111001001010011011011100100","0000011000000111101100100001100","1011001001011000100001011110010","1011000111111000100111101000000","0000100000110000111110000001111","1011001001011000100001011110010","0100010011101000110001011100000","1011001001011000100001011110010","1011111001001010011011011100100","0000011110000010000010110101011","0100000101001111011011001011110","0100101101011010001101101000100","1011010111011010100011101011001","1111101100100111000100010100011","0100100101111111100101001010001"}

Returns: {22, 32768 }
"000"

{"000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000","000"}

Returns: {0, 134217728 }
"010010110111100100110"

{"000011100100110010011","010010011000010001110","011011000000001000000","100110010000001011110","001110111011011001110","001011010000101000101","000010101101100100000","110000110100101011001","110101100111011100011","101001010100110011100","111111010101000110000","110100111101101000100","101010011100100101010","100001000010111100001","101011011000000111100","001110111000011100101","110100101010001111011","100000000101011011100","101001010000110110111","001101111110111011101","001011001001111110100"}

Returns: {18, 1024 }
"110110100001001010011111000000010000010101"

{"011000001101101110101001110011010111110000","011100111011011111111010101011010001110101","011000001101101110101001110011010111110000","011000001101101110101001110011010111110000"}

Returns: {23, 4 }
"10011001001010111100010"

{"00110100100010000011110","10000010010011101010011","10100100111101010001001","00110101011010100100010","11000110001110000001001","00000011010001100000100","01110101111100011001011","11010010111000001000101","01100011100110011000000","00101101110111100000010","01100110011110010100100","00001101010001101010101","11101100001010011011101","11111000100110001100101","00110001111101011010110","10010001010101000000110","00110010000101010101110","01111011011110000010011","00111001000101010010111","01011010011111001100111","10110000101100001110110","01010011101100100011011","10000100001001011111101","00011010111001111101101","01111101100001001001100","00100001011100000101111","01010011101011100101101","01110001101110110011001","01011100011010101110001","00001101000101010100101","00111001100011111011100","10101110110010001110110","10010001001010011111110","01110011001101000011111","01100001001000110110101","00011011110010010101011","10111010001011010011111"}

Returns: {23, 16384 }
"10001010001000101000011100101010001001101"

{"00101100101111100111010110001001111111001","00011111000001011111111110001011111011011","10011010101001011001010100010110101111101","00101001011101010001101011100011100001101","01100011001101111100011010111000011010101","00111101001110011111001010010011001011101","00100101011001000000011011000111000000100","11110010110110110100010001010101100100011","00110110000100000111001011011111010000001","11111001100100100101001110101110110101000","00011011000111111000000001111110101110100","11110101100000110100111110001010010100001","00101111111111000000000110100011011010100","01101001101011111100000111011100000000101","10111110011100000001010011111001101110101","00010111011011100000101111101101000101010","00101011100001101110100111100001000101100","10101101011001001111011101010110110100111","11110011011010101100001101111101100101111","10000110111000100001111010110111110001011","10000000011010110000010111110111001010010","00111011101100001110100111010011110000100","01110000010000111011001010100000001010000","10100110010011010111011100011010101111011","01110101111010000100101001111101011110011","11100111010001101011110010111010000101000","00001101110000000000110010111011101010010"}

Returns: {28, 1572864 }
"1000100100011001100100011110100"

{"1010011100101011111101011100011","0111000011101110111111001110101","0111100110001000101001110101100","1100110011110011101011110010100","1001110010000110101011011111000","1000111011100111110100001101000","0101001010111101100111101110001","0110011011011001100111100111010","0110010100010010000100001101010","0110000011111001101110000001110","1101010100001111101001110110111","1010110001011010011011011011010","0110010100101100001110101010001","0111111101011000100011111011011","1110001100110010000001010111001","0101001100011000000001110100000","1001011101001000001011011001000","1010101010111101111100001101001","0001011111110000100011101010110"}

Returns: {27, 16 }
"01110001111110000101111011010101111111111111001"

{"10010101001111010000000010100110011001001011011","11100011000000001111011110110000011111100100111","11111111100110110000101110110001001101011110011","00101010011001010011111111000000000001000001011","11110100110001011111101110000010110001000111001","00001100011111100011100001001001010010101001010","11110100110001011111101110000010110001000111001","10001001100101010101110111001110111001111001111","01010110110011111100100101001000111000000010001","10101011011111000011010111111010010100101010010","00101011101000101010111100111100101111001010101","00111100011010011100001001011111101100010111001","10110111111001111100100111111011000110010000110","11101111011100001010111010101000100000110011111","11111011011010010110010000001100110011100101111","10011010101000100011111001000001101001100001101","10010101000000001100000010011110000110111101001","10010110110100100110011101011001010110110110101","10010111000101011111011110100101111000111101011","10010111001001100101011011001100001010110101011","11010010111011010101110101100010010000100111000","10001101011010010101001100100010101010111100001","00100110001010001010011011100000100001100000001","00110101000100011010010000111110011100000110001","01101001011110101100110110000001101001100000110","11010100000001000110010010110101111101100010100","10000111110000111001001010000100001010100110101","00010101110100000011101100001001010000100011100","01111111010010111111000000100110011011000000110","01101010101001100000101100010111010100010101000","00111000101001100110110111011010001101011010111","00110000001001000101101101111111001100110110011","10000011001111111001110001101000011001100011011","10010110111000011100011000110000100100111110101","00101010011001010011111111000000000001000001011","10000110001110011100001001000000111011011011001","01010111000010000101100110110100010110001001111"}

Returns: {35, 134217728 }
"0101101100001001010101"

{"1111100001010001100101","1111000111111110000010","0000010000000100010101","0001011101011011110001","0010000111000111001101","0011010010000100110110","1100000001001011101010","0110101001001000001111","0100111110111111010011","1100110100101001111001","1111111000011100111000","0110111110011111100110","1011000001110100111000","0110111000011101011000","1110100100111101110010","1111111101010111100111","1100100110101010110010","0011011111010111100011","1110110011000101001101","0000010110101101010010"}

Returns: {19, 384 }
"1100111011000101001010110110"

{"1111001100100011000000011100","0000000000000000000000000000","1111100111001011000001000000","0100111001110101101111000111","1011110101010110101111011011","1111001100100011000000011100","1011110101010110101111011011","1111100111001011000001000000","0100111001110101101111000111","0100010010011101101110011011","1011110101010110101111011011","1011011110111110101110000111","0100111001110101101111000111","1111100111001011000001000000","0000101011101000000001011100","1011110101010110101111011011","0100111001110101101111000111","1011110101010110101111011011","1011110101010110101111011011","1011011110111110101110000111","0100010010011101101110011011","1111001100100011000000011100","0000101011101000000001011100","1111001100100011000000011100","0000000000000000000000000000","0100111001110101101111000111","0100111001110101101111000111","1011011110111110101110000111","1111001100100011000000011100","0100111001110101101111000111","0000101011101000000001011100","1111100111001011000001000000","0000101011101000000001011100"}

Returns: {16, 2147483648 }
"0"

{"0"}

Returns: {0, 2 }
"0100111010100011111101"

{"1001110101000100111010","0010000111011110101011","0100001101000101100100","0101111011010110001101","1000110011110111111010","0010000111011110101011","1110110110010110001100","1100000001101000001110","0101001011110110100100","0001111001101001010000","1101111000000001011110","1011001101000000000001"}

Returns: {16, 192 }
"111010010010000010011110000"

{"000100110100110001101011111","000110101110010001000011100","001100010100011110101111111","111100111001110000101011111","000101111010011011101001100","100100100010101111010001111","010101111010110000100001110","011100111000011010100100101","110110000011101001100011111","101111100011011000111100101","111010110110100011011100101","100111010010100111110100000","001101010011001111110000100","101001110111111100111000110","101001100011010010000110000","111010000011100100010111100","011010110101110001010011001","000011101001110111011011000","010101000001101010000010101","111010101100111011101000001","011100010011011101000101001","111010000100011111101000010","111100011000000101001100111","101111000001101110001011000","110011110000110100101101001","011101010111001100001100001","011111011100110010100110101","101100111001100011100000011","100011000100010111001010011"}

Returns: {27, 4 }
"10001"

{"11001","00101","10101","00110","00110","01010","11101","01001","11111","00010","10000","00000","01000","00110","00001","01010","10000","01100","10110","01011","10001","01111","01010","11100","11101","01000","01001","11011","00111","11101","01001","01001","00010","11100","11011","11011","11100","00010","01101","00101"}

Returns: {5, 34359738368 }
"10111101011110000100001000"

{"11111001010101111111001111","00010000000010001110110100","00111101100100100010111011","00110111000101010011100111","10001000011011101110010001","10000110000011000011110000","00111101011001001100101101","00011101111011000110011111","00000111000001110011100100","10100001000000100100001111","10010110110010101010001010","01101000100010011001111101","00001010111111110011101101","01100010110011101010010100","01101000111111110111011010","00010000011111111011111011","11100000010011010110101100","00101010101101101100011111","00000000101110011110011100","01001111011000111101001101","10000101001100110100111011"}

Returns: {24, 64 }
"0110011011011111111110010001000100010"

{"1000001101101101111001010010000110101","0000010101010111101011110000001111001","1010111000101110100011010110000011110","1100101011101100001101110011000111010","0001100100110101110010001100000000100","1000101011101111010110110110111101101","0100001011100100010010100111101100101","0101000101100001110000101101100101111","0100100011110101110111000011010101110","0110110111110010011100111011010111101","1001110111001101111111010101111000001","0001101101001110101110001001111111110","0101101001101111001111111000100000100","1111011011111110000110100010011011011","1011100101001010100111011011100000001","1000100011110101011001011101111110011","0000111001100000011001101111000011011","0010101100001011111001000001100010000","0110100100110000010001010110101000111","1010001000011001101000010111111101101","1100101010010001000000110001010110001","0001110010000100010110100011111111010","0100010010111100000000111100011001001","1110110011110100010101110001100110001","0110101010100110010110101101011001001","1000011110001101111100011011011100000"}

Returns: {34, 8 }
"100101100001011100111100010111"

{"000000000000000000000000000000","000000000000000000000000000000","000000000000000000000000000000","000000000000000000000000000000","000000000000000000000000000000","000000000000000000000000000000","000000000000000000000000000000","000001100000110110001000010101","000001100000110110001000010101","000001100000110110001000010101","000000000000000000000000000000","000001100000110110001000010101","000000000000000000000000000000","000001100000110110001000010101"}

Returns: {16, 8192 }
"101110110001011100110111011"

{"010011001111010000101010111","101001001110100100100011000","111010000001110100001001111","101001001110100100100011000","111010000001110100001001111","110010100000101111010000101","110010100000101111010000101","011011101110001011110011101","110010100000101111010000101","101001001110100100100011000","110010100000101111010000101","011011101110001011110011101","000000000000000000000000000","010011001111010000101010111","101001001110100100100011000","111010000001110100001001111","000000000000000000000000000","100001101111111111111010010","010011001111010000101010111","101001001110100100100011000","001000100001011011011001010","000000000000000000000000000","001000100001011011011001010","001000100001011011011001010","100001101111111111111010010","011011101110001011110011101","000000000000000000000000000","001000100001011011011001010","011011101110001011110011101","111010000001110100001001111","100001101111111111111010010","010011001111010000101010111","111010000001110100001001111","000000000000000000000000000"}

Returns: {17, 4294967296 }
"100011011010001111010100001100111011000111110"

{"110111011001110101111010011011111001001010100","100010011100111010100110011101100011110110101","101011000110011100001100000100110010000110010","101110010111101010110100000100011110011000001","111111001101010110011011100010010100011010101","100011110111100110101110100001101110111100000","110100010001100111111111000011011010011010100","101010011010010110010111011100101100010000010","111001100011000101001010110111001101011101111","000001011011010001110010001111000011110111101","100111100011011101010000101111111001010101110","101011001111100010000100010001011001101111100","001100000101100110011010110011110111101111110","000010000001011011001111111011011000011010010","111001000100111101100100000100001010000010000","001010010001110110100101110100111111000100011","110010110010011100100010011100010100001100101","001111011000101111111010101000000001000000101","010011110010011000000111001100100010111101100","110111111101000000000010110001011001011001111","000101011000101110011001001001100000000111011","111101110000011000100111100010000010111110011","011100010010000001000001000100011010001000001","110101110101110010011101101010100110111110000","110011101010110110100001010110111001110110011","010101001000001010100100000000100110110111100","000011000001111000111001100000000110011111011","010110101000001011110110001111110100110001000","100100101010100011011110100000011101100011100","111101111000001110011110001101001110100110011","101000001010011011010001111010111001000011011","001011100100011100110000000000010011111011100","111010101010111100010010001101001011001110111","110111011001111001111010001110000111001111000","111011001011001100010110010001001110111000001"}

Returns: {38, 65536 }
"10111110101"

{"00000000000","00000000000","00000000000","00000000000","11000100101","00000000000","00000000000","11000100101","00000000000","00000000000","11000100101","11000100101","11000100101","00000000000","00000000000","00000000000","11000100101","00000000000","11000100101"}

Returns: {8, 262144 }
"001110110001101111110000"

{"000101101011001011001111","000011001011010110100100","110000101001100110101111","110001111100101001111011","010111111010010001111001","110001010101011010010110","001000111110100110100011","001111100100010110110010","001110111001000100011010","000100011011001111111000","011000100000110011010011","101110000101110001000101","100111111100111101010110","101001110101101001000101","001000000001011011110110","110000001010101011111110","001101100111100100100011","010100100010100011000110","000100000010000011101000","010010000001110011100110","101010100010011110001000"}

Returns: {22, 40 }
"0101001011001001111101000000001001"

{"0100100000001000000010010001101010","0000001110110010011011000011011010","0010111111001000101000000010101001","0110110101011110011100100101011000","1101010100100100010110100101101101","1000011101110000011011011000010010","0110100111010001111010101101011110","0110100111010001111010101101011110","0110000011111101010111011000011111","0001011111111111000100010001010010","0000100100101100101101110101000001","1100011001010100110100111100111001","0010000111011001111000111100110100","1011101111001000010001000011101111","1111111001100011011000101111000010","0000011100111101111101001011011100","1110011110001101001100000000001101","0110001101001111001100011011000101","1110101000101110000111111101001010","1011000101010110100111110101110100","1100001011011011010010110100111111","0100110010000111100100011001101100","1000001111111111111101010000010100","1000010011000010000000011011001000","1111111001100011011000101111000010","0100100000001000000010010001101010","1001111010011110001111110111011101","0101100011001010111011001011100100","0011100000110111101100010011111011","0011001010101001011010100101100000","1110111010100001100001110101001100","1011111101000111110111001011101001","0111000000111111101110000010010001","0110111011101100000111100110000010","0001001101110000100010011001010100","1100000101101001001001110111100101","0000011100111101111101001011011100","1000010011000010000000011011001000","1000111001011100110110101101010011"}

Returns: {24, 4294967296 }
"110010111010101111010111111000101"

{"010011010110101101001000000010110","001011011100010100010100110001011","100010000010110101110011110100000","011001001001110000000010010000011","011001011111011000000110000111001"}

Returns: {21, 3 }
"1100001100111100000010101"

{"0010101000011110000011011","0000011010100000101110001","0100000100100110011100010","0010110101000010000110000","0001101100010110100100001","1101100001001100010000110","1100001110100110101000000","1111011011100111001100110","0011111101011011001011010","0011111001110111101101010","1011001011000000001000010","0010101110110111011000100","1110000111000000001000010","0011011010100010110010100","0000000001011000100110000","1101101110011101110001011","1000010011001101100101101","1000000111010010101011011","1011001111101100011000111","1111011001110111101010000","1101110000000110100101100","0000100100011110111100111","0011000000110110100010000","1000001011100100001001000","0000000011111000110110001","1100011010011000001111100","1010001100110100000101100","0000101110101001001110010","0110010101010001000101010","0000010000011001100010111","1101011000011010110101111","1000100010001011001110010","0000110100100001111001100","0110100010011001010011101","1101011010110100101101000","1110110001000110110111110","0000001001110101010110100","1110011001111101001011011","0101001101000111000001001"}

Returns: {24, 1048576 }
"100100110010111101001111101111010110"

{"010001011000010110101011110100011110","110110110100111000101000011111000101","010101111011111001100001110110101100","111101001110111110110010111110100111","100101010011000110100011100000001010","001000011010101100100101001101011100","111001011001110110110100000100001010","110111001000101011101011011001000100","101011000100100110100111111000111100","100110001101010001000011000001001011","111001001110101101001001000100110110","101011010011010000110111100001001101","001101111101010000101000000001101000","000000000101011101110011001100111110","110110101000001000001010010011011011","111100010100110011111111010001101111","110000011111010101001011111110110010","100001011101011100111000000111010011","100101000010110010100100100001010111","110000110000100011011111101111000100","100100100100010011010010110011100100","110101001100100011100111010011010100","100101010110001001110001101000101101","000101010111100101011111000101001110","101100101100000110110101101111101110","011010010001101001001011010101000000","100001111000011101010010111010001000","100101100010000011010000001001111111","010110110100110111101011001111111101","111000011010000100001001101111111011","111100101111101100011111001101111010","010001101110100000000011111100000101","001010111011001000101110100011011010"}

Returns: {30, 524288 }
"101111101001111100011101101000001000011111111101"

{"110110001111001010111100000110111001100010001001","000010001000100101110000011100100000011111000001","100111100110110110110111111111100001111011100000","000010111100110001111101000101010111111010000011","010011110001010000011111110011110011010011100000","001011011110011011110101100101101010010000011001","110111101110001011000101110001111110100111000100","111111110001100001101100001111100001010010000011","100111010110110111010011111100110100110000100000","100110011110010100001000101111101110101111001011","101100100101100101111010010100100001001001001011","011010100011100011111100110101101011001101010001","010100011111011001110110001010100101010010011100","000111111100111110000011101111101110111110101111","101100100101101001000000001011101111100010011101","000101111010100111000110101001001001100110110011","010011001101101100100001011100010110010010010000","100110110111110011001001001011101110111100101000","010001000101011001010010000110111000011100100111","010101010111000100011111101001011010111011110101","000000110010011101011111010000110111111000101001","010011111001001111000000101101011100101110001110","101101001010101110010011000010001110000101110110","101100011000100111011101111011000011010010001010","001110110110101010001000110110001001100000100010","110000000000010110100110010010000010000111110101","111000011101111101000111100001110011000011110010","100101010111011101100001100001010110011001011101","111011101000010111001111010101011010000110110011","100010010110100000101011111101001011010111011011","111000111111100111111001101111010001011001000110","110010001110110110011011010001100101110101101101","100000101101000011101001010001110001001010010101","110001011011010011000000010110110100100000101001","000001110010111110011010010000010011011101110000","010101011001011100001111111101000000001110010111","110110011101000100111111010001000000001001001111"}

Returns: {45, 10 }
"1011"

{"0000", "0000", "0000" }

Returns: {3, 8 }
"00000000000000000000000000000000000000000000000001"

{"10000000000000000000000001111111111111111111111111", "01000000000000000000000001111111111111111111111111", "00100000000000000000000001111111111111111111111111", "00010000000000000000000001111111111111111111111111", "00001000000000000000000001111111111111111111111111", "00000100000000000000000001111111111111111111111111", "00000010000000000000000001111111111111111111111111", "00000001000000000000000001111111111111111111111111", "00000000100000000000000001111111111111111111111111", "00000000010000000000000001111111111111111111111111", "00000000001000000000000001111111111111111111111111", "00000000000100000000000001111111111111111111111111", "00000000000010000000000001111111111111111111111111", "00000000000001000000000001111111111111111111111111", "00000000000000100000000001111111111111111111111111", "00000000000000010000000001111111111111111111111111", "00000000000000001000000001111111111111111111111111", "00000000000000000100000001111111111111111111111111", "00000000000000000010000001111111111111111111111111", "00000000000000000001000001111111111111111111111111", "00000000000000000000100001111111111111111111111111", "00000000000000000000010001111111111111111111111111", "00000000000000000000001001111111111111111111111111", "00000000000000000000000101111111111111111111111111", "00000000000000000000000011111111111111111111111111" }

Returns: {49, 1 }

Statistics

Problem Statement for "BrightLampsRemake"

Problem Statement

Definition

Constraints

Examples