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Assume further that a number is written in each position of such an n×n square. This square is called "homogeneous" if the sum of the numbers written in n independent positions is the same, no matter how the positions are chosen. Write a program to determine if a given square is homogeneous!
The input contains several test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 1000). Each of the next n lines contains n numbers, separated by exactly one space character. Each number is an integer from the interval [-1000000,1000000].
The last test case is followed by a zero.
For each test case output whether the specified square is homogeneous or not. Adhere to the format shown in the sample output.
2 1 2 3 4 3 1 3 4 8 6 -2 -3 4 0 0
homogeneous not homogeneous