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.

Examples

Input

2 3
AB
1 1
1 2
2 2

Output

Yes

Input

4 3
ABAB
1 2
2 3
3 1

Output

No

Input

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

Output

Yes

Input

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

Output

No

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