#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  long long n, m;
  cin >> n >> m;
  long long q;
  cin >> q;
  long long down[n][m][2];
  long long sum = 0;
  for (long long l = n - 1; l >= 0; --l) {
    for (long long i = m - 1; i >= 0; --i) {
      down[l][i][0] = 1;
      if (l + 1 < n) down[l][i][0] = down[l + 1][i][1] + 1;
      down[l][i][1] = 1;
      if (i + 1 < m) down[l][i][1] = down[l][i + 1][0] + 1;
      sum += down[l][i][0] + down[l][i][1];
    }
  }
  bool blocked[n][m];
  for (long long i = 0; i < n; ++i) {
    for (long long j = 0; j < m; ++j) {
      blocked[i][j] = false;
    }
  }
  long long open = n * m;
  for (long long k = 0; k < q; ++k) {
    long long x, y;
    cin >> x >> y;
    x--;
    y--;
    if (blocked[x][y]) {
      open++;
      long long xx = x;
      long long yy = y;
      long long type = 0;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 1;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
      xx = x;
      yy = y;
      type = 1;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 1;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
    } else {
      open--;
      long long xx = x;
      long long yy = y;
      long long type = 0;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 0;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
      xx = x;
      yy = y;
      type = 1;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 0;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
    }
    blocked[x][y] = !blocked[x][y];
    cout << sum - open << "\n";
  }
}

### Prompt

Create a solution in Cpp for the following problem:

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:

<image>

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  long long n, m;
  cin >> n >> m;
  long long q;
  cin >> q;
  long long down[n][m][2];
  long long sum = 0;
  for (long long l = n - 1; l >= 0; --l) {
    for (long long i = m - 1; i >= 0; --i) {
      down[l][i][0] = 1;
      if (l + 1 < n) down[l][i][0] = down[l + 1][i][1] + 1;
      down[l][i][1] = 1;
      if (i + 1 < m) down[l][i][1] = down[l][i + 1][0] + 1;
      sum += down[l][i][0] + down[l][i][1];
    }
  }
  bool blocked[n][m];
  for (long long i = 0; i < n; ++i) {
    for (long long j = 0; j < m; ++j) {
      blocked[i][j] = false;
    }
  }
  long long open = n * m;
  for (long long k = 0; k < q; ++k) {
    long long x, y;
    cin >> x >> y;
    x--;
    y--;
    if (blocked[x][y]) {
      open++;
      long long xx = x;
      long long yy = y;
      long long type = 0;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 1;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
      xx = x;
      yy = y;
      type = 1;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 1;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
    } else {
      open--;
      long long xx = x;
      long long yy = y;
      long long type = 0;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 0;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
      xx = x;
      yy = y;
      type = 1;
      sum -= down[xx][yy][type];
      down[xx][yy][type] = 0;
      sum += down[xx][yy][type];
      while (xx >= 0 && yy >= 0 && ((xx == x && yy == y) || !blocked[xx][yy])) {
        if (type == 0) {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (xx + 1 < n) down[xx][yy][type] = down[xx + 1][yy][1 - type] + 1;
          sum += down[xx][yy][type];
          yy--;
        } else {
          sum -= down[xx][yy][type];
          if (xx != x || yy != y)
            if (yy + 1 < m) down[xx][yy][type] = down[xx][yy + 1][1 - type] + 1;
          sum += down[xx][yy][type];
          xx--;
        }
        type = 1 - type;
      }
    }
    blocked[x][y] = !blocked[x][y];
    cout << sum - open << "\n";
  }
}

```