Magic Square Formation

Given a positive integer (N) and a list of (N^2) integers, determine whether it is possible to arrange the integers into an (N \times N) grid such that every row, every column, and both main diagonals have the same sum. The required magic sum for each row, column, and diagonal is given by [ \frac{N(N^2+1)}{2} ] Print YES if such an arrangement exists, otherwise print NO.

inputFormat

The input is provided via standard input (stdin) in two lines. The first line contains a single integer (N) representing the size of the square. The second line contains (N^2) space-separated integers.

outputFormat

Output a single line to standard output (stdout): YES if the numbers can be rearranged to form a magic square, otherwise NO.## sample

3
8 1 6 3 5 7 4 9 2

YES