Problem Statement

There is a simple undirected graph with $N$ vertices and $M$ undirected edges, and the vertices are numbered from $1$ to $N$.
If this graph has a simple cycle of length $5$ containing vertex $1$, print $\verb|"YES"|$; otherwise, print $\verb|"NO"|$.

An undirected graph is said to have a simple cycle of length $5$ if there exists a vertex set $(a,b,c,d,e)$ satisfying the following conditions.

• $a,b,c,d,e$ are pairwise distinct
• Vertices $a,b$ are adjacent
• Vertices $b,c$ are adjacent
• Vertices $c,d$ are adjacent
• Vertices $d,e$ are adjacent
• Vertices $e,a$ are adjacent

Input

$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$

Line $1$ contains $2$ integers $N,\;M(2 \leq N \leq 2 \times 10^{4},\; 0 \leq M \leq \text{min}(N(N-1)/2,\;5 \times 10^{4}))$ separated by a space, representing the number of vertices and the number of edges.
Line $2$ begins the following $M$ lines. On the $i(1 \leq i \leq M)$-th of these lines, $2$ integers $A_i, B_i (1\leq A_i, B_i \leq N)$ are given separated by a space, indicating that there is an edge between vertex $A_i$ and vertex $B_i$.
The graph is guaranteed to be simple. That is, there are no self-loops or multiple edges.

Output

Print the answer in $1$ line.

Sample

5 5
1 2
2 3
3 4
4 5
5 1

YES

5 4
1 2
2 3
3 4
4 5

NO

6 6
1 2
2 3
3 4
4 5
5 6
6 2

NO

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

YES

7 10
1 2
1 3
1 4
1 5
2 3
2 4
2 6
3 4
3 7
4 5

YES