Order magic square N is a square matrix of size NxN , composed of numbers 1, 2< /code>, ..., NxN so that the sums for each column, each row and each of the two large diagonals are equal to each other. Write a program that checks if a given square matrix is a magic square.

Input data
The first line enters the size of the matrix N (\(0<N<=100\)) . The following N lines contain matrix rows, each with N values separated by spaces.

Imprint
The program should output the word 'YES' if the matrix is a magic square, and the word 'NO' if it is not.