eolymp
Problems

Regular graph

Regular graph

Time limit 1 second
Memory limit 128 MiB

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 data

First line contains number n (1n100) of vertices and number m (mn (n - 1) / 2) of edges in a graph. Then given m pairs of numbers - the edges of graph.

Output data

Print YES if graph is regular and NO otherwise.

Examples

Input example #1
3 3
1 2
1 3
2 3
Output example #1
YES
Input example #2
3 2
1 2
2 3
Output example #2
NO