#include <bits/stdc++.h>
using namespace std;
const long long maxn = 1e3 + 10;
int dp0[maxn][maxn], dp1[maxn][maxn];
int pd0[maxn][maxn], pd1[maxn][maxn];
bool c[maxn][maxn];
int l, r;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  long long maxx = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      c[i][j] = 1;
      dp0[i][j] = dp1[i][j - 1] + 1;
      dp1[i][j] = dp0[i - 1][j] + 1;
      pd1[i][j] = dp1[i][j];
      pd0[i][j] = dp0[i][j];
      maxx += dp0[i][j] + dp1[i][j] - 1;
    }
  }
  int x, y;
  int vv = 0;
  while (q--) {
    cin >> l >> r;
    x = l, y = r;
    if (c[l][r] == 1) {
      x = l, y = r;
      vv = 0;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 1) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            dp0[x][y] -= dp1[l][r];
            break;
            vv++;
          }
          dp0[x][y] -= dp1[l][r];
          if (vv == 0) {
            maxx -= dp1[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            dp1[x][y] -= dp1[l][r];
            break;
            vv++;
          }
          dp1[x][y] -= dp1[l][r];
          if (vv == 0) {
            maxx -= dp1[l][r];
          }
        }
      }
      vv = 0;
      x = l, y = r;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 0) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] -= dp0[l][r];
            break;
          }
          dp0[x][y] -= dp0[l][r];
          if (vv == 0) {
            maxx -= dp0[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] -= dp0[l][r];
            break;
          }
          dp1[x][y] -= dp0[l][r];
          if (vv == 0) {
            maxx -= dp0[l][r];
          }
        }
      }
      maxx -= (dp0[l][r] + dp1[l][r] - 1);
      cout << maxx << "\n";
      c[l][r] = 0;
    } else if (c[l][r] == 0) {
      x = l, y = r;
      vv = 0;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 1) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] += dp1[l][r];
            break;
          }
          dp0[x][y] += dp1[l][r];
          if (vv == 0) {
            maxx += dp1[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] += dp1[l][r];
            break;
          }
          dp1[x][y] += dp1[l][r];
          if (vv == 0) {
            maxx += dp1[l][r];
          }
        }
      }
      vv = 0;
      x = l, y = r;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 0) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] += dp0[l][r];
            break;
          }
          dp0[x][y] += dp0[l][r];
          if (vv == 0) {
            maxx += dp0[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] += dp0[l][r];
            break;
          }
          dp1[x][y] += dp0[l][r];
          if (vv == 0) {
            maxx += dp0[l][r];
          }
        }
      }
      maxx += (dp0[l][r] + dp1[l][r] - 1);
      cout << maxx << "\n";
      c[l][r] = 1;
    }
  }
}

### 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;
const long long maxn = 1e3 + 10;
int dp0[maxn][maxn], dp1[maxn][maxn];
int pd0[maxn][maxn], pd1[maxn][maxn];
bool c[maxn][maxn];
int l, r;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  long long maxx = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      c[i][j] = 1;
      dp0[i][j] = dp1[i][j - 1] + 1;
      dp1[i][j] = dp0[i - 1][j] + 1;
      pd1[i][j] = dp1[i][j];
      pd0[i][j] = dp0[i][j];
      maxx += dp0[i][j] + dp1[i][j] - 1;
    }
  }
  int x, y;
  int vv = 0;
  while (q--) {
    cin >> l >> r;
    x = l, y = r;
    if (c[l][r] == 1) {
      x = l, y = r;
      vv = 0;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 1) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            dp0[x][y] -= dp1[l][r];
            break;
            vv++;
          }
          dp0[x][y] -= dp1[l][r];
          if (vv == 0) {
            maxx -= dp1[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            dp1[x][y] -= dp1[l][r];
            break;
            vv++;
          }
          dp1[x][y] -= dp1[l][r];
          if (vv == 0) {
            maxx -= dp1[l][r];
          }
        }
      }
      vv = 0;
      x = l, y = r;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 0) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] -= dp0[l][r];
            break;
          }
          dp0[x][y] -= dp0[l][r];
          if (vv == 0) {
            maxx -= dp0[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] -= dp0[l][r];
            break;
          }
          dp1[x][y] -= dp0[l][r];
          if (vv == 0) {
            maxx -= dp0[l][r];
          }
        }
      }
      maxx -= (dp0[l][r] + dp1[l][r] - 1);
      cout << maxx << "\n";
      c[l][r] = 0;
    } else if (c[l][r] == 0) {
      x = l, y = r;
      vv = 0;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 1) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] += dp1[l][r];
            break;
          }
          dp0[x][y] += dp1[l][r];
          if (vv == 0) {
            maxx += dp1[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] += dp1[l][r];
            break;
          }
          dp1[x][y] += dp1[l][r];
          if (vv == 0) {
            maxx += dp1[l][r];
          }
        }
      }
      vv = 0;
      x = l, y = r;
      for (int i = 1; i <= 2000; i++) {
        if (i % 2 == 0) {
          y++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp0[x][y] += dp0[l][r];
            break;
          }
          dp0[x][y] += dp0[l][r];
          if (vv == 0) {
            maxx += dp0[l][r];
          }
        } else {
          x++;
          if (x > n || y > m) {
            break;
          }
          if (c[x][y] == 0) {
            vv++;
            dp1[x][y] += dp0[l][r];
            break;
          }
          dp1[x][y] += dp0[l][r];
          if (vv == 0) {
            maxx += dp0[l][r];
          }
        }
      }
      maxx += (dp0[l][r] + dp1[l][r] - 1);
      cout << maxx << "\n";
      c[l][r] = 1;
    }
  }
}

```