#include <bits/stdc++.h>
using namespace std;
const int N = 1000 + 5;
int n, m, q, hor[N][N], ver[N][N], ans, x, y, ix, jx, v, h, vv, hh;
int main() {
  vector<vector<bool> > free(N, vector<bool>(N, 1));
  scanf("%d%d%d", &n, &m, &q);
  ans = n * m;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      if (j > 0) {
        hor[i][j] = 1;
        if (i > 0) hor[i][j] += hor[i - 1][j - 1];
      }
      if (i > 0) {
        ver[i][j] = 1;
        if (j > 0) ver[i][j] += ver[i - 1][j - 1];
      }
      ans += hor[i][j];
      ans += ver[i][j];
      if (i > 0) ans += hor[i - 1][j];
      if (j > 0) ans += ver[i][j - 1];
    }
  while (q--) {
    scanf("%d%d", &x, &y);
    x--;
    y--;
    if (free[x][y]) {
      ans = ans - hor[x][y] - ver[x][y] - (x > 0 ? hor[x - 1][y] : 0) -
            (y > 0 ? ver[x][y - 1] : 0) - 1;
      h = hor[x][y], v = ver[x][y];
      free[x][y] = hor[x][y] = ver[x][y] = 0;
      ix = 0, jx = 1;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (jx > ix) {
          ans -= hor[x + ix][y + jx];
          ans -= v;
          hh = hor[x + ix][y + jx];
          if (jx == 1) hor[x + ix][y + jx] = 0;
          if (jx > 1) {
            hor[x + ix][y + jx] = 1;
            if (ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        } else {
          ans -= ver[x + ix][y + jx];
          ans -= hh;
          v = ver[x + ix][y + jx];
          if (ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        }
      }
      ix = 1, jx = 0;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (ix > jx) {
          ans -= ver[x + ix][y + jx];
          ans -= h;
          vv = ver[x + ix][y + jx];
          if (ix == 1) ver[x + ix][y + jx] = 0;
          if (ix > 1) {
            ver[x + ix][y + jx] = 1;
            if (jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        } else {
          ans -= hor[x + ix][y + jx];
          ans -= vv;
          h = hor[x + ix][y + jx];
          if (jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        }
      }
    } else {
      if (y > 0 && free[x][y - 1]) {
        hor[x][y] = 1;
        if (x > 0) hor[x][y] += hor[x - 1][y - 1];
      }
      if (x > 0 && free[x - 1][y]) {
        ver[x][y] = 1;
        if (y > 0) ver[x][y] += ver[x - 1][y - 1];
      }
      ans = ans + hor[x][y] + ver[x][y] + (x > 0 ? hor[x - 1][y] : 0) +
            (y > 0 ? ver[x][y - 1] : 0) + 1;
      v = h = 0;
      free[x][y] = 1;
      ix = 0, jx = 1;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (jx > ix) {
          ans -= hor[x + ix][y + jx];
          ans -= v;
          hh = hor[x + ix][y + jx];
          if (y + jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (x + ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        } else {
          ans -= ver[x + ix][y + jx];
          ans -= hh;
          v = ver[x + ix][y + jx];
          if (x + ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (y + jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        }
      }
      ix = 1, jx = 0;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (ix > jx) {
          ans -= ver[x + ix][y + jx];
          ans -= h;
          vv = ver[x + ix][y + jx];
          if (x + ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (y + jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        } else {
          ans -= hor[x + ix][y + jx];
          ans -= vv;
          h = hor[x + ix][y + jx];
          if (y + jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (x + ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        }
      }
    }
    printf("%d\n", ans);
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to 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 int N = 1000 + 5;
int n, m, q, hor[N][N], ver[N][N], ans, x, y, ix, jx, v, h, vv, hh;
int main() {
  vector<vector<bool> > free(N, vector<bool>(N, 1));
  scanf("%d%d%d", &n, &m, &q);
  ans = n * m;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      if (j > 0) {
        hor[i][j] = 1;
        if (i > 0) hor[i][j] += hor[i - 1][j - 1];
      }
      if (i > 0) {
        ver[i][j] = 1;
        if (j > 0) ver[i][j] += ver[i - 1][j - 1];
      }
      ans += hor[i][j];
      ans += ver[i][j];
      if (i > 0) ans += hor[i - 1][j];
      if (j > 0) ans += ver[i][j - 1];
    }
  while (q--) {
    scanf("%d%d", &x, &y);
    x--;
    y--;
    if (free[x][y]) {
      ans = ans - hor[x][y] - ver[x][y] - (x > 0 ? hor[x - 1][y] : 0) -
            (y > 0 ? ver[x][y - 1] : 0) - 1;
      h = hor[x][y], v = ver[x][y];
      free[x][y] = hor[x][y] = ver[x][y] = 0;
      ix = 0, jx = 1;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (jx > ix) {
          ans -= hor[x + ix][y + jx];
          ans -= v;
          hh = hor[x + ix][y + jx];
          if (jx == 1) hor[x + ix][y + jx] = 0;
          if (jx > 1) {
            hor[x + ix][y + jx] = 1;
            if (ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        } else {
          ans -= ver[x + ix][y + jx];
          ans -= hh;
          v = ver[x + ix][y + jx];
          if (ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        }
      }
      ix = 1, jx = 0;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (ix > jx) {
          ans -= ver[x + ix][y + jx];
          ans -= h;
          vv = ver[x + ix][y + jx];
          if (ix == 1) ver[x + ix][y + jx] = 0;
          if (ix > 1) {
            ver[x + ix][y + jx] = 1;
            if (jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        } else {
          ans -= hor[x + ix][y + jx];
          ans -= vv;
          h = hor[x + ix][y + jx];
          if (jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        }
      }
    } else {
      if (y > 0 && free[x][y - 1]) {
        hor[x][y] = 1;
        if (x > 0) hor[x][y] += hor[x - 1][y - 1];
      }
      if (x > 0 && free[x - 1][y]) {
        ver[x][y] = 1;
        if (y > 0) ver[x][y] += ver[x - 1][y - 1];
      }
      ans = ans + hor[x][y] + ver[x][y] + (x > 0 ? hor[x - 1][y] : 0) +
            (y > 0 ? ver[x][y - 1] : 0) + 1;
      v = h = 0;
      free[x][y] = 1;
      ix = 0, jx = 1;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (jx > ix) {
          ans -= hor[x + ix][y + jx];
          ans -= v;
          hh = hor[x + ix][y + jx];
          if (y + jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (x + ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        } else {
          ans -= ver[x + ix][y + jx];
          ans -= hh;
          v = ver[x + ix][y + jx];
          if (x + ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (y + jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        }
      }
      ix = 1, jx = 0;
      while (free[x + ix][y + jx] && x + ix < n && y + jx < m) {
        if (ix > jx) {
          ans -= ver[x + ix][y + jx];
          ans -= h;
          vv = ver[x + ix][y + jx];
          if (x + ix > 0) {
            ver[x + ix][y + jx] = 1;
            if (y + jx > 0) ver[x + ix][y + jx] += ver[x + ix - 1][y + jx - 1];
            ans += ver[x + ix][y + jx];
            ans += hor[x + ix - 1][y + jx];
          }
          jx++;
        } else {
          ans -= hor[x + ix][y + jx];
          ans -= vv;
          h = hor[x + ix][y + jx];
          if (y + jx > 0) {
            hor[x + ix][y + jx] = 1;
            if (x + ix > 0) hor[x + ix][y + jx] += hor[x + ix - 1][y + jx - 1];
            ans += hor[x + ix][y + jx];
            ans += ver[x + ix][y + jx - 1];
          }
          ix++;
        }
      }
    }
    printf("%d\n", ans);
  }
  return 0;
}

```