Bobo has a directed acyclic graph (DAG) with $n$ nodes and $m$ edges whose nodes is conveniently labeled with $1, 2, \dots, n$. 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.
Input
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 $a_i, b_i$.
The $i$-th of the last $q$ lines contains an integer $v_i$.
- $2 \leq n \leq 300$
- $1 \leq m \leq \frac{n(n - 1)}{2}$
- $1 \leq q \leq 300$
- $1 \leq a_i < b_i \leq n$
- $1 \leq v_i \leq n$
- The number of tests cases does not exceed $10$.
Output
For each operation, output an integer which denotes the number of pairs.
Sample Input
3 3 2 2 3 1 3 1 2 1 1
Sample Output
1 3