### Homogeneous squares

#### Problem Description

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*, where

_{2},y_{2})*1 ≤ x*, are called "independent" if they occupy different rows and different columns, that is,

_{1},y_{1},x_{2},y_{2}≤ n*x*and

_{1}≠x_{2}*y*. More generally,

_{1}≠y_{2}*n*positions are called independent if they are pairwise independent. It follows that there are

*n!*different ways to choose

*n*independent positions.

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!

#### Input

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.

#### Output

For each test case output whether the specified square is homogeneous or not. Adhere to the format shown in the sample output.

#### Sample Input

2 1 2 3 4 3 1 3 4 8 6 -2 -3 4 0 0

#### Sample Output

homogeneous not homogeneous