Time Limit: 3000 ms
Memory Limit: 65535 ms
Assume you have a square of size n that is divided into n×n positions just as a checkerboard. Two positions (x1,y1) and (x2,y2), where 1 ≤ x1,y1,x2,y2 ≤ n, are called "independent" if they occupy different rows and different columns, that is, x1≠x2 and y1≠y2. 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.
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!