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Ethan wants to draw a painting on an m×n board. He can draw some strips on the board using a paintbrush of width one. In each step, he must choose a new color and paint a full column or a full row.
He has a great image to be drawn on the board, but he doesn’t know which color to use first. You must help him in finding out the order of colors.
There are multiple test cases in the input. The first line of each test case contains two integers m and n, the size of the board (0< m, n <100). Following the first line, there are m lines with n integers denoting the color in each cell. All the colors are positive integer numbers less than 10000. The input is terminated with a single line containing two consecutive zeros.
For each test case, write a single line containing the order of colors used to paint the board. If there are several answers, output the one which is lexicographically smallest (considering each number as a symbol).
4 4 1 5 4 3 6 5 6 6 2 2 2 2 1 5 4 3 3 2 1 1 2 3 2 3 0 0
1 3 4 6 5 2 2 3 1
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