Is it a Tree?

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

Input

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

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

Examples