Problem Statement

You are given a graph consisting of $N$ vertices and $M$ undirected edges.

The $i$-th vertex has one of the characters P,D,C,A written on it.
The $j$-th edge connects the $u_j$-th vertex and the $v_j$-th vertex.

A way of going from one vertex to another in which the start and end vertices are different and no vertex is visited more than once is called a path.
A path of length 3 is a path consisting of 3 edges and 4 vertices.

A path of length 3 is called a PDCA path if, when its vertices are traversed from one end to the other, they can be read as PDCA.

Among the paths of length 3 in the graph, how many PDCA paths are there? Find the count modulo $10^9+7$.

Input

N M
S
u_1 v_1
...
u_M v_M

$2 \le N \le 10^5$
$0 \le M \le 10^5$
$|S| = N$
$1 \le u_i \lt v_i \le N$
The given graph does not contain multiple edges or self-loops.
Each character of the string $S$ is one of P,D,C,A.
The $i$-th character of $S$ indicates the character written on vertex number $i$.

Output

Output the number of PDCA paths modulo 1000000007.

Print a newline at the end.

Sample

7 11
PAAPCDD
1 3
1 5
1 6
2 5
2 6
3 5
5 6
4 5
5 7
4 7
2 7

4

6 3
ACPPPD
1 2
3 4
4 5

0

11 11
AAACCCDDPPP
1 4
1 5
2 5
4 7
5 7
7 9
7 10
2 4
3 6
6 8
8 11

9