Bobo has a directed acyclic graph (DAG) with n nodes and m edges whose nodes is conveniently labeled
with 1, 2, . . . , n. All nodes are white initially.
Bobo performs q operations subsequently. The i-th operation is to change the node v_i from white to black
or vice versa.
After each operation, he would like to know the number of pairs of nodes (u, v) that u, v are both white and
there exists a path from u to v passing only white nodes.

The input contains zero or more test cases and is terminated by end-of-file. For each test case:
The first line contains three integers n,m and q.
The i-th of the following m lines contains two integers ai, bi.
The i-th of the last q lines contains an integer vi.
• 2 ≤ n ≤ 300
• 1 ≤ m ≤ n(n−1)/2
• 1 ≤ q ≤ 300
• 1 ≤ a_i < b_i ≤ n
• 1 ≤ v_i ≤ n
• The number of tests cases does not exceed 10.

3 3 2
2 3
1 3
1 2
1
1

1
3

2017年四川省赛