Competitions

# Graph representation

# 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** ≤ **n** ≤ **100**) of vertices and number **m** (**m** ≤ **n** (**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.

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