human
Write me a Python code to print the number of different staircases after each query given the following:
PYTHON3 solution for "You are given a matrix, consisting of n rows and m columns. The rows are numbered top to bottom, the columns are numbered left to right.

Each cell of the matrix can be either free or locked.

Let's call a path in the matrix a staircase if it: 

  * starts and ends in the free cell.

  * visits only free cells.

  * has one of the two following structures: 
    1. the second cell is 1 to the right from the first one, the third cell is 1 to the bottom from the second one, the fourth cell is 1 to the right from the third one, and so on.

    2. the second cell is 1 to the bottom from the first one, the third cell is 1 to the right from the second one, the fourth cell is 1 to the bottom from the third one, and so on. 


In particular, a path, consisting of a single cell, is considered to be a staircase.

Here are some examples of staircases:


Initially all the cells of the matrix are free.

You have to process q queries, each of them flips the state of a single cell. So, if a cell is currently free, it makes it locked, and if a cell is currently locked, it makes it free.

Print the number of different staircases after each query. Two staircases are considered different if there exists such a cell that appears in one path and doesn't appear in the other path.

Input

The first line contains three integers n, m and q (1 ≤ n, m ≤ 1000.
1 ≤ q ≤ 10^4) — the sizes of the matrix and the number of queries.

Each of the next q lines contains two integers x and y (1 ≤ x ≤ n.
1 ≤ y ≤ m) — the description of each query.

Output

Print q integers — the i-th value should be equal to the number of different staircases after i queries. Two staircases are considered different if there exists such a cell that appears in one path and doesn't appear in the other path.

Examples

Input

2 2 8
1 1
1 1
1 1
2 2
1 1
1 2
2 1
1 1

Output

5
10
5
2
5
3
1
0

Input

3 4 10
1 4
1 2
2 3
1 2
2 3
3 2
1 3
3 4
1 3
3 1

Output

49
35
24
29
49
39
31
23
29
27

Input

1000 1000 2
239 634
239 634

Output

1332632508
1333333000":
assistant
#Here is Python code to print the number of different staircases after each query.
 def main():
    H, W, Q = map(int, input().split());A = [[] for _ in range(H + W)]
    for i in range(H):
        for j in range(W):A[(i + j + 1) // 2 * 2].append(0);A[(i + j) // 2 * 2 + 1].append(0)
    RawAns = H * W;Diff = [0] * (H + W)
    for i in range(H + W):K = len(A[i]) * (len(A[i]) - 1) // 2;Diff[i] = K;RawAns += K
    for _ in range(Q):
        h, w = map(int, input().split());h -= 1;w = W - w
        i1 = (h + w + 1) // 2 * 2;j1 = h * 2 + (h + w) % 2 if i1 < W else (W - w - 1) * 2 + (h + w + 1) % 2
        i2 = (h + w) // 2 * 2 + 1;j2 = h * 2 + (h + w + 1) % 2 if i2 < W else (W - w - 1) * 2 + (h + w) % 2
        if A[i1][j1]: RawAns += 1
        else: RawAns -= 1
        A[i1][j1] ^= 1;A[i2][j2] ^= 1;Tmp1 = 0;Count = -1
        for a in A[i1]:
            if a:Tmp1 += Count * (Count + 1) // 2;Count = -1
            else: Count += 1
        Tmp1 += Count * (Count + 1) // 2;Tmp2 = 0;Count = -1
        for a in A[i2]:
            if a:Tmp2 += Count * (Count + 1) // 2;Count = -1
            else: Count += 1
        Tmp2 += Count * (Count + 1) // 2;RawAns -= Diff[i1] - Tmp1 + Diff[i2] - Tmp2;Diff[i1] = Tmp1;Diff[i2] = Tmp2;print(RawAns)
if __name__ == '__main__':main()