Bobo has a directed acyclic graph (DAG) with n nodes and m edges whose nodes is conveniently labeled with .
All nodes are white initially.

Bobo performs q operations subsequently.
The i-th operation is to change the node 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 .
The i-th of the last q lines contains an integer .

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* The number of tests cases does not exceed 10.

For each operation, output an integer which denotes the number of pairs.

3 3 2
2 3
1 3
1 2
1
1

1
3