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Time Limit: 3.0 Seconds Memory Limit: 65536K

Total Runs: 136 Accepted Runs: 73

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 *(x*_{2},y_{2}),
where *1 ≤ x*_{1},y_{1},x_{2},y_{2} ≤ n,
are called "independent" if they occupy different rows and different columns,
that is, *x*_{1}≠x_{2} and
*y*_{1}≠y_{2}. More generally, *n* positions are
called independent if they are pairwise independent. It follows that there are
*n*! different ways to choose *n* independent positions.
### Input Specification

### Output Specification

### Sample Input

### Sample Output

### Hint

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

Huge input

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