Bobo has an undirected graph with n vertices and m edges. The vertices are numbered by 1, \dots, n, and the i-th edge is between the a_i-th and the b_i-th vertex. Plus, the i-th vertex is associated with a character c_i.

Find the number of ways to choose four distinct vertices (u, v, w, x) such that

• u and v, v and w, w and x are connected by an edge,
• c_u = \mathtt{b}, c_v = \mathtt{o}, c_w = \mathtt{b}, c_x = \mathtt{o}.

Note from SCNUOJ admin: we don't have the official test data sets, and all tests used here are randomly generated, so expect weak tests and/or even wrong input format. Contact one of the admins if you wish to improve the tests.

The input consists of several test cases terminated by end-of-file. For each test case,

The first line contains two integers n and m.

The second line contains n characters c_1 \dots c_n.

For the following m lines, the i-th line contains two integers a_i and b_i.

• 4 \le n \le 2 \times 10^5
• 0 \le m \le 2 \times 10^5
• c_i \in {\mathtt{b}, \mathtt{o}} for each 1 \leq i \leq n
• 1 \leq a_i, b_i \leq n for each 1 \leq i \leq m
• a_i \neq b_i for each 1 \leq i \leq m
• {a_i, b_i} \neq {a_j, b_j} for each 1 \leq i < j \leq m
• In each input, the sum of n does not exceed 2 \times 10^5. The sum of m does not exceed 2 \times 10^5.

For each test case, output an integer which denotes the number of ways.

For the first test case, there are 2 quadrangles (1, 3, 4, 5), (2, 3, 4, 5).

For the second test case, there are 4 quadrangles (1, 2, 3, 4), (1, 4, 3, 2), (3, 2, 1, 4), (3, 4, 1, 2).

For the third test case, there are no valid quadrangles.