Checking for an undirected graph

For a given square matrix n x n of zeros and ones determine whether it can be the adjacency matrix of a simple undirected graph. The simple graph does not contain loops and multiple edges.

Input

The first line contains the value of n (1 ≤ n ≤ 100). Each of the next n lines contains n numbers, describing the adjacency matrix.

Output

Print YES, if the graph is simple undirected and NO otherwise.

Examples