#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class T>
bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <class T>
bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
template <class T>
std::ostream &operator<<(std::ostream &out, const std::vector<T> &arr) {
  std::cout << "{";
  for (int i = 0; i < arr.size(); i++) std::cout << (!i ? "" : ", ") << arr[i];
  std::cout << "}";
  return out;
}
template <class T>
std::ostream &operator<<(std::ostream &out,
                         const std::vector<std::vector<T>> &arr) {
  std::cout << "{\n";
  for (auto &vec : arr) std::cout << "  " << vec << ",\n";
  std::cout << "}";
  return out;
}
template <class S, class T>
std::ostream &operator<<(std::ostream &out, const std::pair<S, T> &p) {
  std::cout << "{" << p.first << "," << p.second << "}" << '\n';
  return out;
}
template <class T>
std::istream &operator>>(std::istream &in, std::vector<T> &arr) {
  for (auto &i : arr) std::cin >> i;
  return in;
}
template <class S, class T>
std::istream &operator>>(std::istream &in, std::pair<S, T> &p) {
  std::cin >> p.first >> p.second;
  return in;
}
template <class T>
void debug_a(T *a, int N) {
  std::cout << "debug array : {";
  for (int i = 0; i < N; i++) {
    std::cout << *(a + i) << (i < N - 1 ? ", " : "}\n");
  }
}
struct io {
  io() {
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(12);
  }
} ioboost;
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  auto inside = [&](int x, int y) {
    return x >= 0 && x < n && y >= 0 && y < m;
  };
  vector<vector<int>> state(n, vector<int>(m, 0));
  function<int(int, int, int, int, int)> func = [&](int x, int y, int dx,
                                                    int dy, int tmp) {
    if (!inside(x, y) || state[x][y]) {
      return tmp;
    }
    return func(x - dx, y + dy, !dx, !dy, tmp + 1);
  };
  function<int(int, int, int, int, int)> func2 = [&](int x, int y, int dx,
                                                     int dy, int tmp) {
    if (!inside(x, y) || state[x][y]) {
      return tmp;
    }
    return func2(x + dx, y - dy, !dx, !dy, tmp + 1);
  };
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      ans++;
      int d = min(n - i, m - j);
      int fi = i + d - 1;
      int fj = j + d - 1;
      int k = 4 * (d - 1);
      if (fi != n - 1 || fj != m - 1) {
        k++;
      }
      ans += k;
    }
  }
  for (int _ = 0; _ < q; _++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    x = (n - 1 - x);
    if (state[x][y]) {
      state[x][y] = 0;
      ll f, g;
      f = func(x, y, 0, 1, 0) - 1;
      g = func2(x, y, 1, 0, 0) - 1;
      if (f or g) {
        ans += f * g + f + g;
      }
      f = func(x, y, 1, 0, 0) - 1;
      g = func2(x, y, 0, 1, 0) - 1;
      if (f or g) {
        ans += f * g + f + g;
      }
      ans++;
    } else {
      ll f, g;
      f = func(x, y, 0, 1, 0) - 1;
      g = func2(x, y, 1, 0, 0) - 1;
      if (f or g) {
        ans -= f * g + f + g;
      }
      f = func(x, y, 1, 0, 0) - 1;
      g = func2(x, y, 0, 1, 0) - 1;
      if (f or g) {
        ans -= f * g + f + g;
      }
      ans--;
      state[x][y] = 1;
    }
    cout << ans << endl;
  }
}

### 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;
using ll = long long;
template <class T>
bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <class T>
bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
template <class T>
std::ostream &operator<<(std::ostream &out, const std::vector<T> &arr) {
  std::cout << "{";
  for (int i = 0; i < arr.size(); i++) std::cout << (!i ? "" : ", ") << arr[i];
  std::cout << "}";
  return out;
}
template <class T>
std::ostream &operator<<(std::ostream &out,
                         const std::vector<std::vector<T>> &arr) {
  std::cout << "{\n";
  for (auto &vec : arr) std::cout << "  " << vec << ",\n";
  std::cout << "}";
  return out;
}
template <class S, class T>
std::ostream &operator<<(std::ostream &out, const std::pair<S, T> &p) {
  std::cout << "{" << p.first << "," << p.second << "}" << '\n';
  return out;
}
template <class T>
std::istream &operator>>(std::istream &in, std::vector<T> &arr) {
  for (auto &i : arr) std::cin >> i;
  return in;
}
template <class S, class T>
std::istream &operator>>(std::istream &in, std::pair<S, T> &p) {
  std::cin >> p.first >> p.second;
  return in;
}
template <class T>
void debug_a(T *a, int N) {
  std::cout << "debug array : {";
  for (int i = 0; i < N; i++) {
    std::cout << *(a + i) << (i < N - 1 ? ", " : "}\n");
  }
}
struct io {
  io() {
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(12);
  }
} ioboost;
int main() {
  int n, m, q;
  cin >> n >> m >> q;
  auto inside = [&](int x, int y) {
    return x >= 0 && x < n && y >= 0 && y < m;
  };
  vector<vector<int>> state(n, vector<int>(m, 0));
  function<int(int, int, int, int, int)> func = [&](int x, int y, int dx,
                                                    int dy, int tmp) {
    if (!inside(x, y) || state[x][y]) {
      return tmp;
    }
    return func(x - dx, y + dy, !dx, !dy, tmp + 1);
  };
  function<int(int, int, int, int, int)> func2 = [&](int x, int y, int dx,
                                                     int dy, int tmp) {
    if (!inside(x, y) || state[x][y]) {
      return tmp;
    }
    return func2(x + dx, y - dy, !dx, !dy, tmp + 1);
  };
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      ans++;
      int d = min(n - i, m - j);
      int fi = i + d - 1;
      int fj = j + d - 1;
      int k = 4 * (d - 1);
      if (fi != n - 1 || fj != m - 1) {
        k++;
      }
      ans += k;
    }
  }
  for (int _ = 0; _ < q; _++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    x = (n - 1 - x);
    if (state[x][y]) {
      state[x][y] = 0;
      ll f, g;
      f = func(x, y, 0, 1, 0) - 1;
      g = func2(x, y, 1, 0, 0) - 1;
      if (f or g) {
        ans += f * g + f + g;
      }
      f = func(x, y, 1, 0, 0) - 1;
      g = func2(x, y, 0, 1, 0) - 1;
      if (f or g) {
        ans += f * g + f + g;
      }
      ans++;
    } else {
      ll f, g;
      f = func(x, y, 0, 1, 0) - 1;
      g = func2(x, y, 1, 0, 0) - 1;
      if (f or g) {
        ans -= f * g + f + g;
      }
      f = func(x, y, 1, 0, 0) - 1;
      g = func2(x, y, 0, 1, 0) - 1;
      if (f or g) {
        ans -= f * g + f + g;
      }
      ans--;
      state[x][y] = 1;
    }
    cout << ans << endl;
  }
}

```