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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(1000000)
N,M=map( int, raw_input().split() )
S=raw_input()

C=[ [0 for i in range(2) ] for j in range(N+1)  ] 	#C[i][0] A no kazu , C[i][1] B no kazu
nl=[ set() for i in range(N+1) ]
D=[ 0 for i in range(N+1) ]		#Mukouka flag   1:delete

for i in range(M):
	a,b=map(int, raw_input().split() )
	nl[a].add(b)
	nl[b].add(a)

	if a==b:
		if S[a-1]=="A": 
			C[a][0]+=1			
		elif S[a-1]=="B":
			C[a][1]+=1			
	else:
		if S[a-1]=="A": 
			C[b][0]+=1
		elif S[a-1]=="B":
			C[b][1]+=1
		if S[b-1]=="A": 
			C[a][0]+=1
		elif S[b-1]=="B":
			C[a][1]+=1


def func(i):
#	print "i,C::",i,C,nl
	if D[i]==1: return
	a_cnt=C[i][0]
	b_cnt=C[i][1]

	if a_cnt==0 or b_cnt==0:
		D[i]=1	#Mukouka flag wo on
		for x in nl[i]:
			if D[x]==1: continue

			if a_cnt>0: C[x][0]-=1;C[i][0]-=1
			elif b_cnt>0: C[x][1]-=1;C[i][1]-=1
			if C[x][0]==0 or C[x][1]==0:
				func(x)


for i in range(1,N+1):
	func(i)



for i,x in enumerate(D):
	if i==0:continue
	if x==0:
		for u in nl[i]:
			if D[u]==0:
				print "Yes"
				quit()
else:
	print "No"