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A time schedule is represented by a 0-1 matrix with n lines and m columns. Each line represents a person and each column an event. All the persons participating to an event have a one in the corresponding entry of their line. Persons not attending the event have a zero entry in that column. Events occur consecutively. Write a program that finds a smart permutation of the events where each person attends all its events in a row. In other words, permute the columns of the matrix so that all ones are consecutive in each line. Input The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs. The first line of the input consists in the number n ≤ 400 of lines. The second line contains m ≤ 400, the number of columns. Then comes the n lines of the matrix. Each line consists in m characters ‘0’ or ‘1’. The input matrix is chosen so that there exists only one smart permutation which preserves column 0 in position 0. To make things easier, any two columns share few common one entries. Output For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.
2/3 The output consists of m numbers indicating the smart permutation of the columns. The first number must be 0 as column 0 does not move. The second number indicate the index (in the input matrix) of the second column, and so on. Sample Input 3 3 4 0110 0001 1101 6 5 01010 01000 10101 10100 00011 00101 21 20 00101000000000000000 10010010010110010100 00101101000000000000 01000000000000001000 00000101100000100000 01000000100000100000 00000010000110000000 01000000000001001000 00000000001001000011 00001000000000000000 10000000000000000100 00010010011000010011 01111101111001111011 01000000000001101011 01100101100001101001 00100101100000000000 00010000001001000011 01010000101001111011 00000010010010010000 00010010011111010111 00101001000000000000 Sample Output 0 3
3/3 1 2 0 2 4 3 1 0 17 11 12 6 9 15 3 10 18 19 13 16 1 14 8 5 7 2 4