Complete graph

An undirected graph is called complete, if any pair of distinct vertices is connected by at least one edge. Given a list of graph edges, check whether the graph is complete.

Input

The first line contains the number of vertices $n(1\le n\le 100)$ and the number of edges $m(1\le m\le 10^4)$ in the graph. Then $m$ pairs of numbers are given, representing the graph edges.

Output

Print "YES" if the graph is complete and "NO" otherwise.

Examples