Check if the Graph is a Crown

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.

profound.academy-graph-crown.drawio.png

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.

Examples

Input

Output

4 4 1 2 2 3 3 1 1 4

No

7 11 3 4 2 3 2 4 1 3 1 4 7 3 7 4 6 3 6 4 5 3 5 4

Yes

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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