Magic Square Verification

In this problem, you are given a square grid of integers. Your task is to determine whether the grid is a magic square or not.

A grid is considered a magic square if:

• All rows sum to the same value.
• All columns sum to the same value.
• The main diagonal (top-left to bottom-right) and the secondary diagonal (top-right to bottom-left) also sum to that same value.

If the grid is empty, it is not considered a magic square. Note that a single element grid is always magic.

Input and Output via standard input (stdin) and standard output (stdout) are required.

inputFormat

The input begins with an integer n representing the number of rows (and columns) in the grid. If n = 0, it means the grid is empty.

If n > 0, the next n lines each contain n integers separated by spaces representing a row of the grid.

For example:

3
2 7 6
9 5 1
4 3 8

outputFormat

Output a single line: YES if the grid is a magic square and NO otherwise.

## sample

3
2 7 6
9 5 1
4 3 8

YES