#include <bits/stdc++.h>
using namespace std;
const int N = 1005;
long long down[N][N], rit[N][N], ans;
int flag[N][N], n, m;
void fun(int x, int y, int f) {
  int a = x, b = y;
  int xia, zuo;
  if (f == -1) {
    xia = rit[a][b] + 1;
    zuo = down[a][b] + 1;
    xia = xia * f;
    zuo = zuo * f;
    ans--;
    ans = ans - rit[a][b] - down[a][b];
    rit[a][b] = down[a][b] = 0;
  } else if (f == 1) {
    ans++;
    rit[a][b] = down[a][b + 1] + (flag[a][b + 1] != 1 && (b + 1 <= m));
    down[a][b] = rit[a + 1][b] + (flag[a + 1][b] != 1 && (a + 1 <= n));
    ans = ans + rit[a][b] + down[a][b];
    xia = rit[a][b] + 1;
    zuo = down[a][b] + 1;
  }
  int now = 0;
  while (1) {
    if (now == 0) {
      a = a - 1;
      if (a < 1 || flag[a][b] == 1) break;
      down[a][b] = down[a][b] + xia;
      ans = ans + xia;
    } else {
      b = b - 1;
      if (b < 1 || flag[a][b] == 1) break;
      rit[a][b] = rit[a][b] + xia;
      ans = ans + xia;
    }
    now = now ^ 1;
  }
  now = 1;
  a = x;
  b = y;
  while (1) {
    if (now == 0) {
      a = a - 1;
      if (a < 1 || flag[a][b] == 1) break;
      down[a][b] = down[a][b] + zuo;
      ans = ans + zuo;
    } else {
      b = b - 1;
      if (b < 1 || flag[a][b] == 1) break;
      rit[a][b] = rit[a][b] + zuo;
      ans = ans + zuo;
    }
    now = now ^ 1;
  }
  printf("%lld\n", ans);
}
void solve() {
  int i, j, q, x, y;
  scanf("%d%d%d", &n, &m, &q);
  for (i = n; i >= 1; --i) {
    for (j = m; j >= 1; --j) {
      if (i == n)
        down[i][j] == 0;
      else
        down[i][j] = down[i][j] + 1 + rit[i + 1][j];
      if (j == m)
        rit[i][j] == 0;
      else
        rit[i][j] = rit[i][j] + 1 + down[i][j + 1];
    }
  }
  ans = 0;
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= m; ++j) {
      ans = ans + down[i][j] + rit[i][j];
    }
  }
  ans = ans + n * m;
  for (i = 1; i <= q; ++i) {
    scanf("%d%d", &x, &y);
    if (flag[x][y] == 1) {
      flag[x][y] = 0;
      fun(x, y, 1);
    } else {
      flag[x][y] = 1;
      fun(x, y, -1);
    }
  }
  return;
}
int main() { solve(); }

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 = 1005;
long long down[N][N], rit[N][N], ans;
int flag[N][N], n, m;
void fun(int x, int y, int f) {
  int a = x, b = y;
  int xia, zuo;
  if (f == -1) {
    xia = rit[a][b] + 1;
    zuo = down[a][b] + 1;
    xia = xia * f;
    zuo = zuo * f;
    ans--;
    ans = ans - rit[a][b] - down[a][b];
    rit[a][b] = down[a][b] = 0;
  } else if (f == 1) {
    ans++;
    rit[a][b] = down[a][b + 1] + (flag[a][b + 1] != 1 && (b + 1 <= m));
    down[a][b] = rit[a + 1][b] + (flag[a + 1][b] != 1 && (a + 1 <= n));
    ans = ans + rit[a][b] + down[a][b];
    xia = rit[a][b] + 1;
    zuo = down[a][b] + 1;
  }
  int now = 0;
  while (1) {
    if (now == 0) {
      a = a - 1;
      if (a < 1 || flag[a][b] == 1) break;
      down[a][b] = down[a][b] + xia;
      ans = ans + xia;
    } else {
      b = b - 1;
      if (b < 1 || flag[a][b] == 1) break;
      rit[a][b] = rit[a][b] + xia;
      ans = ans + xia;
    }
    now = now ^ 1;
  }
  now = 1;
  a = x;
  b = y;
  while (1) {
    if (now == 0) {
      a = a - 1;
      if (a < 1 || flag[a][b] == 1) break;
      down[a][b] = down[a][b] + zuo;
      ans = ans + zuo;
    } else {
      b = b - 1;
      if (b < 1 || flag[a][b] == 1) break;
      rit[a][b] = rit[a][b] + zuo;
      ans = ans + zuo;
    }
    now = now ^ 1;
  }
  printf("%lld\n", ans);
}
void solve() {
  int i, j, q, x, y;
  scanf("%d%d%d", &n, &m, &q);
  for (i = n; i >= 1; --i) {
    for (j = m; j >= 1; --j) {
      if (i == n)
        down[i][j] == 0;
      else
        down[i][j] = down[i][j] + 1 + rit[i + 1][j];
      if (j == m)
        rit[i][j] == 0;
      else
        rit[i][j] = rit[i][j] + 1 + down[i][j + 1];
    }
  }
  ans = 0;
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= m; ++j) {
      ans = ans + down[i][j] + rit[i][j];
    }
  }
  ans = ans + n * m;
  for (i = 1; i <= q; ++i) {
    scanf("%d%d", &x, &y);
    if (flag[x][y] == 1) {
      flag[x][y] = 0;
      fun(x, y, 1);
    } else {
      flag[x][y] = 1;
      fun(x, y, -1);
    }
  }
  return;
}
int main() { solve(); }

```