Competitions

# 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

The first line contains the number of vertices n (1n100) in the graph. In the next lines the adjacency matrix of size n × 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

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

Time limit 1 second
Memory limit 128 MiB
Input example #1
3
0 1 0
1 0 1
0 1 0

Output example #1
YES