#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  srand(chrono::steady_clock::now().time_since_epoch().count());
  ;
  long long n, m, q;
  cin >> n >> m >> q;
  vector<vector<bool>> g(n, vector<bool>(m));
  long long ans = n * m;
  long long h = 1, w = 2;
  long long flag = 0;
  while (h <= n && w <= m) {
    ans += (n - h + 1) * (m - w + 1);
    if (flag == 0)
      h++;
    else
      w++;
    flag = 1 - flag;
  }
  h = 2;
  w = 1;
  flag = 1;
  while (h <= n && w <= m) {
    ans += (n - h + 1) * (m - w + 1);
    if (flag == 0)
      h++;
    else
      w++;
    flag = 1 - flag;
  }
  while (q--) {
    long long x, y;
    cin >> x >> y;
    x--;
    y--;
    long long xori = x, yori = y;
    long long delta = -1;
    long long a1 = 1;
    flag = 0;
    while (true) {
      if (flag == 0)
        x--;
      else
        y--;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a1++;
      } else
        break;
    }
    flag = 0;
    x = xori;
    y = yori;
    long long a2 = 1;
    while (true) {
      if (flag == 0)
        y++;
      else
        x++;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a2++;
      } else
        break;
    }
    delta += a1 * a2;
    a1 = 1;
    flag = 0;
    x = xori;
    y = yori;
    while (true) {
      if (flag == 0)
        y--;
      else
        x--;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a1++;
      } else
        break;
    }
    a2 = 1;
    flag = 0;
    x = xori;
    y = yori;
    while (true) {
      if (flag == 0)
        x++;
      else
        y++;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a2++;
      } else
        break;
    }
    delta += a1 * a2;
    x = xori;
    y = yori;
    if (g[x][y]) {
      ans += delta;
      g[x][y] = false;
    } else {
      ans -= delta;
      g[x][y] = true;
    }
    cout << ans << '\n';
  }
}

### Prompt

Please formulate 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;
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  srand(chrono::steady_clock::now().time_since_epoch().count());
  ;
  long long n, m, q;
  cin >> n >> m >> q;
  vector<vector<bool>> g(n, vector<bool>(m));
  long long ans = n * m;
  long long h = 1, w = 2;
  long long flag = 0;
  while (h <= n && w <= m) {
    ans += (n - h + 1) * (m - w + 1);
    if (flag == 0)
      h++;
    else
      w++;
    flag = 1 - flag;
  }
  h = 2;
  w = 1;
  flag = 1;
  while (h <= n && w <= m) {
    ans += (n - h + 1) * (m - w + 1);
    if (flag == 0)
      h++;
    else
      w++;
    flag = 1 - flag;
  }
  while (q--) {
    long long x, y;
    cin >> x >> y;
    x--;
    y--;
    long long xori = x, yori = y;
    long long delta = -1;
    long long a1 = 1;
    flag = 0;
    while (true) {
      if (flag == 0)
        x--;
      else
        y--;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a1++;
      } else
        break;
    }
    flag = 0;
    x = xori;
    y = yori;
    long long a2 = 1;
    while (true) {
      if (flag == 0)
        y++;
      else
        x++;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a2++;
      } else
        break;
    }
    delta += a1 * a2;
    a1 = 1;
    flag = 0;
    x = xori;
    y = yori;
    while (true) {
      if (flag == 0)
        y--;
      else
        x--;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a1++;
      } else
        break;
    }
    a2 = 1;
    flag = 0;
    x = xori;
    y = yori;
    while (true) {
      if (flag == 0)
        x++;
      else
        y++;
      flag = 1 - flag;
      if (0 <= x && x < n && 0 <= y && y < m && !g[x][y]) {
        a2++;
      } else
        break;
    }
    delta += a1 * a2;
    x = xori;
    y = yori;
    if (g[x][y]) {
      ans += delta;
      g[x][y] = false;
    } else {
      ans -= delta;
      g[x][y] = true;
    }
    cout << ans << '\n';
  }
}

```