Problem:
Score : 900 points

Problem Statement

You are given an undirected graph consisting of N vertices and M edges.
The vertices are numbered 1 to N, and the edges are numbered 1 to M.
In addition, each vertex has a label, A or B. The label of Vertex i is s_i.
Edge i bidirectionally connects vertex a_i and b_i.

The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.
Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.

For example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2, the resulting string is ABABB.

Determine if Nusook can make all strings consisting of A and B.

Constraints

2 \leq N \leq 2 \times 10^{5}

1 \leq M \leq 2 \times 10^{5}

|s| = N

s_i is A or B.

1 \leq a_i, b_i \leq N

The given graph may NOT be simple or connected.

Input

Input is given from Standard Input in the following format:

N M
s
a_1 b_1
:
a_{M} b_{M}

Output

If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.

Sample Input 1

2 3
AB
1 1
1 2
2 2

Sample Output 1

Yes

Since Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.

Sample Input 2

4 3
ABAB
1 2
2 3
3 1

Sample Output 2

No

For example, Nusook cannot make BB.

The given graph may not be connected.

Sample Input 3

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9

Sample Output 3

Yes

Sample Input 4

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11

Sample Output 4

No

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Node
    {
        private readonly char item;
        public bool exists = true;
        public List<Node> edges = new List<Node>();
        public Node(char c)
        {
            item = c;
        }
        public bool Good()
        {
            return edges.Any(edge => edge.item == 'A')
                && edges.Any(edge => edge.item == 'B');
        }
    }
    class Program
    {
        static bool Solve(int N, Node[] nodes)
        {
            var q = new Queue<Node>();
            foreach (var node in nodes)
            {
                if (!node.Good()) { q.Enqueue(node); }
            }
            while (q.Count > 0)
            {
                var node = q.Dequeue();
                if (node.exists && !node.Good())
                {
                    for (int i = 0; i < node.edges.Count; ++i)
                    {
                        var child = node.edges[i];
                        child.edges.Remove(node);
                        q.Enqueue(child);
                    }
                    node.exists = false;
                }
            }
            return nodes.Any(node => node.exists);
        }
        static void Main(string[] args)
        {
            int[] V1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int N = V1[0];
            int M = V1[1];
            string s = Console.ReadLine();
            var nodes = new Node[N];
            for (int i = 0; i < N; ++i) { nodes[i] = new Node(s[i]); }
            for (int i = 0; i < M; ++i)
            {
                int[] V2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                var a = nodes[V2[0] - 1];
                var b = nodes[V2[1] - 1];
                a.edges.Add(b);
                b.edges.Add(a);
            }
            Console.WriteLine(Solve(N, nodes) ? "Yes" : "No");
        }
    }
}