Problem:
Score : 800 points

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.

Notes

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.

Sample Input 1

7 9
1 2
1 3
2 3
1 4
1 5
4 5
1 6
1 7
6 7

Sample Output 1

Yes

Three circuits can be formed using each of the edges exactly once, as follows:

Sample Input 2

3 3
1 2
2 3
3 1

Sample Output 2

No

Three circuits are needed.

Sample Input 3

18 27
17 7
12 15
18 17
13 18
13 6
5 7
7 1
14 5
15 11
7 6
1 9
5 4
18 16
4 6
7 2
7 11
6 3
12 14
5 2
10 5
7 8
10 15
3 15
9 8
7 15
5 16
18 15

Sample Output 3

Yes

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
    {
    	static void Main(string[] args)
    	{
            string[] s0 = Console.ReadLine().Split(' ');
            int n = int.Parse(s0[0]);
            int m = int.Parse(s0[1]);
            int[] count = new int[n];
            for (int i=0; i<m; i++)
            {
                string[] s = Console.ReadLine().Split(' ');
                count[int.Parse(s[0]) - 1] ++;
                count[int.Parse(s[1]) - 1] ++;
            }
            int ans = 0;
            foreach (int i in count)
            {
                if (i%2 == 1)
                {
                    Console.WriteLine("NO");
                    return;
                }
                if (i == 4) ans++;
                if (i >= 6) ans += 2;
            }
            if (ans >= 2) Console.WriteLine("YES");
            else Console.WriteLine("NO");
            

            
            
        }
    }
    //mcs Main.cs
    //mono Main.exe