Regular graph

Undirected graph is called regular, if all its vertices have the same degree.

Graph is given by list of edges. Check, is it regular.

Input

First line contains number $n(1\le n\le 100)$ of vertices and number $m(m\le n\cdot (n-1)/2)$ of edges in a graph. Then given $m$ pairs of numbers — the edges of graph.

Output

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

Examples