3499: Greedy Petya
[Creator : ]
Description
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputPetya is an unexperienced programming contestant. Recently he has come across the following problem:
You are given a non-directed graph which consists of n nodes and m edges. Your task is to determine whether the graph contains a Hamiltonian path.
Petya wrote a quick bug-free code which he believes solves this problem. After that Petya decided to give this problem for April Fools Day contest. Unfortunately, Petya might have made a mistake, and it's quite possible that his algorithm is wrong. But this isn't a good excuse to leave the contest without submitting this problem, is it?
Input
The first line contains two integers n,m (1≤n≤20;0≤m≤400). Next m lines contain pairs of integers vi,ui (1≤vi,ui≤n).
Output
Follow the format of Petya's code output.
Examples
Input
2 3
1 2
2 1
1 1
Output
Yes
Input
3 0
Output
No
Input
10 20
3 10
4 6
4 9
7 5
8 8
3 10
9 7
5 2
9 2
10 6
10 4
1 1
7 2
8 4
7 2
1 8
5 4
10 2
8 5
5 2
Output
No