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Problem
Given a square matrix, determine if it is a "magic square": the sum of every row, every column, and both main diagonals are equal. Print "YES" or "NO".
Input format
Input
input.txt
- An integer N (1 ≤ N ≤ 20) - N rows with N integers
Output format
Output
output.txt
- "YES" or "NO"
Example
input
3 8 1 6 3 5 7 4 9 2
output
YES
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Sample cases (from the problem)
Sample Case 1
Input
3 8 1 6 3 5 7 4 9 2
Expected output
YES
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