Is the matrix symmetric?

A matrix is called symmetric if the opposite numbers around the main diagonal are equal.

Given an n×nn \times n matrix, our task is to find out if the matrix is symmetric.

The first line of the input contains a single integer n. The next n lines contain n integers which represent the matrix.

The output of the program should contain a single line - yes if the matrix is symmetric and no otherwise.

Input

Output

3
0 1 2
1 8 3
2 3 4

yes

3
0 0 0
0 0 0
1 0 1

no

Constraints

Time limit: 1.6 seconds

Memory limit: 512 MB

Output limit: 1 MB