#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class T, class U>
inline bool chmax(T& a, U b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class U>
inline bool chmin(T& a, U b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
constexpr int INF = 1000000000;
constexpr ll llINF = 3000000000000000000;
constexpr int mod = 998244353;
constexpr double eps = 1e-10;
const double pi = acos(-1);
int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};
int Random(int mi, int ma) {
  random_device rnd;
  mt19937 mt(rnd());
  uniform_int_distribution<int> engine(mi, ma);
  return engine(mt);
}
bool prime(int a) {
  if (a == 1) return false;
  for (int i = 2; i * i <= a; i++) {
    if (a % i == 0) return false;
  }
  return true;
}
vector<int> primes;
void init_prime(int n) {
  primes.push_back(2);
  for (int i = 3; i <= n; i += 2) {
    bool f = true;
    for (int j : primes) {
      if (j * j > i) break;
      if (i % j == 0) {
        f = false;
        break;
      }
    }
    if (f) primes.push_back(i);
  }
}
ll modpow(ll a, ll b, ll m = mod) {
  ll res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      res %= m;
    }
    a *= a;
    a %= m;
    b >>= 1;
  }
  return res;
}
vector<ll> inv, fact, factinv;
void init_fact(int n) {
  inv.resize(n + 1);
  fact.resize(n + 1);
  factinv.resize(n + 1);
  inv[0] = 0;
  inv[1] = 1;
  fact[0] = 1;
  factinv[0] = 1;
  for (ll i = 1; i <= n; i++) {
    if (i >= 2) inv[i] = mod - ((mod / i) * inv[mod % i] % mod);
    fact[i] = (fact[i - 1] * i) % mod;
    factinv[i] = factinv[i - 1] * inv[i] % mod;
  }
}
ll _inv(ll a, ll m = mod) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}
ll comb(int a, int b) {
  if (a < b) return 0;
  if (a < 0) return 0;
  return fact[a] * factinv[a - b] % mod * factinv[b] % mod;
}
bool flag[1010][1010];
int a[1010][1010];
ll ans = 0;
void solve() {
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = n - 1; i >= 0; i--) {
    for (int j = m - 1; j >= 0; j--) {
      a[i][j] = (i + 1 < n && j + 1 < m ? a[i + 1][j + 1] : 0) + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (j + 1 < m)
        ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
      if (i + 1 < n)
        ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
    }
  }
  ans += n * m;
  while (q--) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    if (flag[x][y]) {
      ans++;
      flag[x][y] = false;
      for (int i = x, j = y; i >= 0 && j >= 0 && !flag[i][j]; i--, j--) {
        if (i < x) {
          if (j + 1 < m)
            ans -= min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
          if (i + 1 < n)
            ans -= min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
          if (j && !flag[i][j - 1])
            ans -= min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
          if (i && !flag[i - 1][j])
            ans -= min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        }
        a[i][j] = (i + 1 < n && j + 1 < m ? a[i + 1][j + 1] : 0) + 1;
        if (j + 1 < m)
          ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
        if (i + 1 < n)
          ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
        if (j && !flag[i][j - 1])
          ans += min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
        if (i && !flag[i - 1][j])
          ans += min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
      }
    } else {
      ans--;
      for (int i = x, j = y; i >= 0 && j >= 0 && !flag[i][j]; i--, j--) {
        if (j + 1 < m)
          ans -= min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
        if (i + 1 < n)
          ans -= min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
        if (j && !flag[i][j - 1])
          ans -= min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
        if (i && !flag[i - 1][j])
          ans -= min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        a[i][j] = (i == x ? 0 : a[i + 1][j + 1] + 1);
        if (i < x) {
          if (j + 1 < m)
            ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
          if (i + 1 < n)
            ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
          if (j && !flag[i][j - 1])
            ans += min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
          if (i && !flag[i - 1][j])
            ans += min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        }
      }
      flag[x][y] = true;
    }
    cout << ans << endl;
  }
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
}

### 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;
using ll = long long;
template <class T, class U>
inline bool chmax(T& a, U b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class U>
inline bool chmin(T& a, U b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
constexpr int INF = 1000000000;
constexpr ll llINF = 3000000000000000000;
constexpr int mod = 998244353;
constexpr double eps = 1e-10;
const double pi = acos(-1);
int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};
int Random(int mi, int ma) {
  random_device rnd;
  mt19937 mt(rnd());
  uniform_int_distribution<int> engine(mi, ma);
  return engine(mt);
}
bool prime(int a) {
  if (a == 1) return false;
  for (int i = 2; i * i <= a; i++) {
    if (a % i == 0) return false;
  }
  return true;
}
vector<int> primes;
void init_prime(int n) {
  primes.push_back(2);
  for (int i = 3; i <= n; i += 2) {
    bool f = true;
    for (int j : primes) {
      if (j * j > i) break;
      if (i % j == 0) {
        f = false;
        break;
      }
    }
    if (f) primes.push_back(i);
  }
}
ll modpow(ll a, ll b, ll m = mod) {
  ll res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      res %= m;
    }
    a *= a;
    a %= m;
    b >>= 1;
  }
  return res;
}
vector<ll> inv, fact, factinv;
void init_fact(int n) {
  inv.resize(n + 1);
  fact.resize(n + 1);
  factinv.resize(n + 1);
  inv[0] = 0;
  inv[1] = 1;
  fact[0] = 1;
  factinv[0] = 1;
  for (ll i = 1; i <= n; i++) {
    if (i >= 2) inv[i] = mod - ((mod / i) * inv[mod % i] % mod);
    fact[i] = (fact[i - 1] * i) % mod;
    factinv[i] = factinv[i - 1] * inv[i] % mod;
  }
}
ll _inv(ll a, ll m = mod) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}
ll comb(int a, int b) {
  if (a < b) return 0;
  if (a < 0) return 0;
  return fact[a] * factinv[a - b] % mod * factinv[b] % mod;
}
bool flag[1010][1010];
int a[1010][1010];
ll ans = 0;
void solve() {
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = n - 1; i >= 0; i--) {
    for (int j = m - 1; j >= 0; j--) {
      a[i][j] = (i + 1 < n && j + 1 < m ? a[i + 1][j + 1] : 0) + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (j + 1 < m)
        ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
      if (i + 1 < n)
        ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
    }
  }
  ans += n * m;
  while (q--) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    if (flag[x][y]) {
      ans++;
      flag[x][y] = false;
      for (int i = x, j = y; i >= 0 && j >= 0 && !flag[i][j]; i--, j--) {
        if (i < x) {
          if (j + 1 < m)
            ans -= min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
          if (i + 1 < n)
            ans -= min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
          if (j && !flag[i][j - 1])
            ans -= min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
          if (i && !flag[i - 1][j])
            ans -= min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        }
        a[i][j] = (i + 1 < n && j + 1 < m ? a[i + 1][j + 1] : 0) + 1;
        if (j + 1 < m)
          ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
        if (i + 1 < n)
          ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
        if (j && !flag[i][j - 1])
          ans += min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
        if (i && !flag[i - 1][j])
          ans += min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
      }
    } else {
      ans--;
      for (int i = x, j = y; i >= 0 && j >= 0 && !flag[i][j]; i--, j--) {
        if (j + 1 < m)
          ans -= min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
        if (i + 1 < n)
          ans -= min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
        if (j && !flag[i][j - 1])
          ans -= min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
        if (i && !flag[i - 1][j])
          ans -= min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        a[i][j] = (i == x ? 0 : a[i + 1][j + 1] + 1);
        if (i < x) {
          if (j + 1 < m)
            ans += min(a[i][j], a[i][j + 1]) * 2 + (a[i][j] > a[i][j + 1]) - 1;
          if (i + 1 < n)
            ans += min(a[i][j], a[i + 1][j]) * 2 + (a[i][j] > a[i + 1][j]) - 1;
          if (j && !flag[i][j - 1])
            ans += min(a[i][j - 1], a[i][j]) * 2 + (a[i][j - 1] > a[i][j]) - 1;
          if (i && !flag[i - 1][j])
            ans += min(a[i - 1][j], a[i][j]) * 2 + (a[i - 1][j] > a[i][j]) - 1;
        }
      }
      flag[x][y] = true;
    }
    cout << ans << endl;
  }
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
}

```