Problems
Is it a Tree?
Is it a Tree?
Undirected graph without loops and multiple edges is given with the adjacency matrix. Determine whether the graph is a tree.
Input data
The first line contains the number of vertices n~(1 \le n \le 100) in the graph. In the next lines the adjacency matrix of size n \cdot n is given, where 1 denotes the presence of an edge, and 0 its absence. The matrix is symmetric with respect to the main diagonal.
Output data
Print the message "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