Description

00000000000000000011
11111111000000000000
00000000000000001111
00000000000011000000
00000000000000111100
00000000000001110000
00111000000000000000
00000000000111000000
00000000111100000000
00000000000000000001
11000000000000000000
00001111111000000000
00000111111111111111
00000000011111100000
00000000001111111110
00000000000000011110
00000001111100000000
00000011111111110000
00011110000000000000
01111111111100000000
00000000000000000111

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. Problem

Problem 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 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

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.

3
4
0110
0001
1101

0
3
1
2

Hint

Sample input2

6 5 01010 01000 10101 10100 00011 00101 Sample output2 0 2 4 3 1 Sample input3 21 20 00101000000000000000 10010010010110010100 00101101000000000000 01000000000000001000 00000101100000100000 01000000100000100000 00000010000110000000 01000000000001001000 00000000001001000011 00001000000000000000 10000000000000000100 00010010011000010011 01111101111001111011 01000000000001101011 01100101100001101001 00100101100000000000 00010000001001000011 01010000101001111011 00000010010010010000 00010010011111010111 00101001000000000000 Sample output3 0 17 11 12 6 9 15 3 10 18 19 13 16 1 14 8 5 7 2 4

Source

Southwestern Europe 2005