Given a simple undirected graph, determine whether there exist two simple cycles of the same length.
Input
The first line contains two positive integers $n$ and $m$, representing the number of vertices and the number of edges, respectively.
The next $m$ lines each contain two positive integers describing an edge.
Output
If such cycles exist, output Yes; otherwise, output No.
Examples
Input 1
10000 0
Output 1
No
Input 2
5 6 1 2 2 3 3 1 1 4 4 5 5 1
Output 2
Yes
Subtasks
For all test cases, $1\le n \le 10^4$ and $1\le m \le 10^6$.
| Subtask ID | $n\leq$ | Score |
|---|---|---|
| $1$ | $10$ | $40$ |
| $2$ | $20$ | $20$ |
| $3$ | $400$ | $20$ |
| $4$ | $10000$ | $20$ |