Split into Two Teams

Medium#graphs #bfs #bipartite· solved by 0 · time limit 2.0 s

Each pair u v means members $u$ and $v$ must be on different teams. Can all $n$ members be split into two teams following every rule? Print Yes or No. (Is the graph bipartite?)

Input

$n$ and $m$ , then $m$ lines u v.

Output

Yes or No.

Constraints

$1 \le n \le 10^5$ , $0 \le m \le 2 \times 10^5$

Sample 1

Input

Output

Yes

Sample 2

Input

Output

No