Assume you have a square of size *n* that is divided into *n×n* positions just as a checkerboard. Two positions *(x _{1},y_{1})* and

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.

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