Description

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