Baobab

Input

The input begins with a single natural number $N$ (N \leq 100), representing the number of vertices in the graph. Following this, there are $N$ lines, each containing $N$ numbers, which form the adjacency matrix of the graph. In the $i$-th row and $j$-th column, a $1$ indicates that vertices $i$ and $j$ are connected by an edge, while a $0$ indicates no edge between them. The main diagonal of the matrix consists of zeros, and the matrix is symmetric about the main diagonal.

Output

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

Examples