Competitions

# Depth First Search

# 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** (**1** ≤ **n** ≤ **100**) 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.

Input example #1

3 0 1 0 1 0 1 0 1 0

Output example #1

YES