Rotational Magic Square Verification

You are given an odd integer n and an n x n grid filled with integers. A magic square is a square matrix in which the sum of every row, every column, and both main diagonals are equal.

Your task is to determine whether the given grid is a magic square. In the problem statement, it is mentioned that you may rotate any row or column in a cyclic manner. However, for the purpose of this problem, you only need to check whether the grid already is a magic square (i.e. no rotations are required).

For a magic square of size n, if we denote the grid as \(a_{ij}\) for \(0 \leq i,j < n\), then there exists a constant \(S\) such that: \[ \sum_{j=0}^{n-1} a_{ij} = S, \quad \sum_{i=0}^{n-1} a_{ij} = S, \quad \sum_{i=0}^{n-1} a_{ii} = S, \quad \sum_{i=0}^{n-1} a_{i,n-1-i} = S \]

Return "YES" if the grid is a magic square, otherwise return "NO".

inputFormat

The input is read from stdin and has the following format:

The first line contains an integer n (the size of the grid).
The following n lines each contain n space-separated integers representing a row of the grid.

outputFormat

Output a single line to stdout containing "YES" if the input grid is a magic square, or "NO" otherwise.

3
8 1 6
3 5 7
4 9 2

YES