Matrix product

Input

Each test case starts with an integer $n$ (n \leq 500). Then three matrices A, B, C are given, each described by $n$ lines containing exactly $n$ integers. Elements of matrices A and B do not exceed $1000$ in absolute value. The last test case contains n = 0 and should not be processed. For example, in the first test case you should check the equality

Output

For each test case, output "YES" or "NO" on a separate line, depending on whether A $\times$ B = C holds or not.

Examples