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Problems

Is it a Tree?

Is it a Tree?

Time limit 1 second
Memory limit 128 MiB

An undirected graph without loops and multiple edges is given by an adjacency matrix. Determine whether this graph is a tree.

Input data

The first line contains the number of vertices n~(1 \le n \le 100) in the graph. Then, an adjacency matrix of size n \times n is given, where 1 indicates the presence of an edge, and 0 indicates its absence. The matrix is symmetric with respect to the main diagonal.

Output data

Print "YES" if the graph is a tree, and "NO" otherwise.

Examples

Input example #1
3
0 1 0
1 0 1
0 1 0
Output example #1
YES