description: 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
solution: #include <bits/stdc++.h>
  using namespace std;
  const long long N = 1005;
  long long n, m, q, ans;
  bool vizitat[N][N];
  long long dp[N][N][2];
  bool verifica(long long i, long long j) {
    if (i < 1 || j < 1 || i > n || j > m) return false;
    return true;
  }
  long long cnt(long long i, long long j) {
    long long answer = 0;
    for (long long it = 0; it <= 1; it++) {
      long long up = 0;
      long long lin = i;
      long long col = j;
      while (verifica(lin, col) && vizitat[lin][col] == false) {
        if (up % 2 == it) {
          lin--;
        } else {
          col--;
        }
        up++;
      }
      long long down = 0;
      lin = i;
      col = j;
      while (verifica(lin, col) && vizitat[lin][col] == false) {
        if (down % 2 == it) {
          col++;
        } else {
          lin++;
        }
        down++;
      }
      answer += up * down;
    }
    answer--;
    return answer;
  }
  int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> n >> m >> q;
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= m; j++) {
        dp[i][j][1] = dp[i][j - 1][0] + 1;
        dp[i][j][0] = dp[i - 1][j][1] + 1;
        ans += dp[i][j][1];
        ans += dp[i][j][0];
      }
    }
    ans -= n * m;
    while (q--) {
      long long lin, col;
      cin >> lin >> col;
      if (vizitat[lin][col] == true) {
        vizitat[lin][col] = false;
        ans += cnt(lin, col);
      } else {
        ans -= cnt(lin, col);
        vizitat[lin][col] = true;
      }
      cout << ans << '\n';
    }
    return 0;
  }
  