Given an undirected graph with v vertices and e edges, you are asked to determine if it’s a star graph. A star graph is a graph that has a central vertex that is connected to all the other vertices, while all the other vertices are only connected to the central one and no other vertex.

Input

The first line of the input contains two integers v (1 ≤ v ≤ 100 000) and e (1 ≤ e ≤ 100 000).

The following e lines contain pairs of integers v1, v2 (1 ≤ v1, v2 ≤ v) which means that the vertex v1 is connected to the vertex v2 and vice versa.

Output

The program should print Yes if the graph is a star graph and No otherwise.