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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

N, M = [int(i) for i in input().split(' ')]
import sys
input = sys.stdin.readline
from collections import defaultdict
sys.setrecursionlimit(10**7)

s = input().strip()
ds = [defaultdict(set), defaultdict(set)]
for ll in sys.stdin:
    i, j = ll.strip().split(' ')
    i, j = int(i)-1, int(j)-1
    x = 0 if s[i] == s[j] else 1
    y = 1 if s[i] == s[j] else 0
    ds[x][str(x) + str(i)].add(str(y) + str(j))
    ds[x][str(x) + str(j)].add(str(y) + str(i))


checked = set()

path = set()

def walk(i, depth):
    dd = ds[depth]
    checked.add(i)
    if i not in dd:
        return False
    for item in dd[i]:
        if item in path:
            return True
        if item not in checked:
            path.add(item)
            if walk(item, (depth+1) % 2):
                return True
            path.remove(item)
    return False

for item in ds[0].keys():
    if item not in checked:
        path.add(item)
        if walk(item, 0):
            print('Yes')
            break
        path.remove(item)
else:
    print('No')