Graph tournament

A directed graph is called a tournament if there is exactly one edge between any pair of its different vertices. Graph is given by the list of edges. Check if it is a tournament.

Input

The first line contains number of vertices $n(1\le n\le 100)$ and number of edges $m(1\le m\le n\cdot (n-1)/2)$ in the graph. The next $m$ lines contain the pairs of numbers — the edges of the graph.

Output

Print "YES" if graph is tournament and "NO" otherwise.

Examples