Given an undirected graph with v vertices and e edges, you are asked to check if it’s a crown graph. A crown consists of a base and may have any number of spikes. The Crown's base consists of a single edge connecting two nodes, and it is a common edge for all the spikes, every spike has only one node connected to both sides of the base.

Input

The first line of the input contains two integers v (1 ≤ v ≤ 1000) and e (1 ≤ e ≤ 10 000).

The following e lines contain pairs of integers v1, v2 (1 ≤ v1, v2 ≤ v) representing an edge between v1 and v2.

Output

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