Problem Statement

You are given a simple connected undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$.

Edge $i$ connects Vertex $a_i$ and $b_i$ bidirectionally.

Determine if three circuits (see Notes) can be formed using each of the edges exactly once.

Note

A circuit is a cycle allowing repetitions of vertices but not edges.

Constraints

• All values in input are integers.
• $1 \leq N,M \leq 10^{5}$
• $1 \leq a_i, b_i \leq N$
• The given graph is simple and connected.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

If three circuits can be formed using each of the edges exactly once, print Yes; if they cannot, print No.