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;
  long long t = 1, n, m, k, q, l, r, ans, a[1009][1009], dy[1009][1009],
            xy[1009][1009], zt[1009][1009], b, c, u, v, x, y, z, mod = 1e9 + 7;
  string s;
  struct st {
    long long x, y;
  };
  bool cmp(const st &a, const st &b) { return a.x < b.x; }
  inline long long read() {
    long long s = 0, w = 1;
    char ch = getchar();
    while (ch > '9' || ch < '0') {
      if (ch == '-') w = -1;
      ch = getchar();
    }
    while (ch <= '9' && ch >= '0')
      s = (s << 1) + (s << 3) + (ch ^ 48), ch = getchar();
    return s * w;
  }
  long long qp(long long x, long long y) {
    long long a = 1, b = x;
    while (y) {
      if (y & 1) a = a * b % mod;
      b = b * b % mod, y >>= 1;
    }
    return a;
  }
  void add(long long x, long long y, bool opt) {
    if (opt) {
      bool wtf = 0;
      long long nx = x, ny = y, posx = -1, posy = -1, asd = 1;
      while (1) {
        if (!wtf)
          nx += 1;
        else
          ny += 1;
        if (nx > n || ny > m) break;
        if (!zt[nx][ny]) {
          if (!wtf)
            posx = nx - 1, posy = ny;
          else
            posx = nx, posy = ny - 1;
          break;
        }
        asd += 1, wtf ^= 1;
      }
      wtf = 1;
      long long nx2 = x, ny2 = y, posx2 = -1, posy2 = -1, asd2 = 1;
      while (1) {
        if (!wtf)
          nx2 -= 1;
        else
          ny2 -= 1;
        if (nx2 < 1 || ny2 < 1) break;
        if (!zt[nx2][ny2]) {
          if (!wtf)
            posx2 = nx2 + 1, posy2 = ny2;
          else
            posx2 = nx2, posy2 = ny2 + 1;
          break;
        }
        asd2 += 1, wtf ^= 1;
      }
      ans += asd * asd2;
      wtf = 1;
      nx = x, ny = y, posx = -1, posy = -1, asd = 1;
      while (1) {
        if (!wtf)
          nx += 1;
        else
          ny += 1;
        if (nx > n || ny > m) break;
        if (!zt[nx][ny]) {
          if (!wtf)
            posx = nx - 1, posy = ny;
          else
            posx = nx, posy = ny - 1;
          break;
        }
        asd += 1, wtf ^= 1;
      }
      wtf = 0;
      nx2 = x, ny2 = y, posx2 = -1, posy2 = -1, asd2 = 1;
      while (1) {
        if (!wtf)
          nx2 -= 1;
        else
          ny2 -= 1;
        if (nx2 < 1 || ny2 < 1) break;
        if (!zt[nx2][ny2]) {
          if (!wtf)
            posx2 = nx2 + 1, posy2 = ny2;
          else
            posx2 = nx2, posy2 = ny2 + 1;
          break;
        }
        asd2 += 1, wtf ^= 1;
      }
      ans += asd * asd2, ans -= 1;
    } else {
      bool wtf = 0;
      long long nx = x, ny = y, posx = -1, posy = -1, asd = 1;
      while (1) {
        if (!wtf)
          nx += 1;
        else
          ny += 1;
        if (nx > n || ny > m) break;
        if (!zt[nx][ny]) {
          if (!wtf)
            posx = nx - 1, posy = ny;
          else
            posx = nx, posy = ny - 1;
          break;
        }
        asd += 1, wtf ^= 1;
      }
      wtf = 1;
      long long nx2 = x, ny2 = y, posx2 = -1, posy2 = -1, asd2 = 1;
      while (1) {
        if (!wtf)
          nx2 -= 1;
        else
          ny2 -= 1;
        if (nx2 < 1 || ny2 < 1) break;
        if (!zt[nx2][ny2]) {
          if (!wtf)
            posx2 = nx2 + 1, posy2 = ny2;
          else
            posx2 = nx2, posy2 = ny2 + 1;
          break;
        }
        asd2 += 1, wtf ^= 1;
      }
      ans -= asd * asd2;
      wtf = 1;
      nx = x, ny = y, posx = -1, posy = -1, asd = 1;
      while (1) {
        if (!wtf)
          nx += 1;
        else
          ny += 1;
        if (nx > n || ny > m) break;
        if (!zt[nx][ny]) {
          if (!wtf)
            posx = nx - 1, posy = ny;
          else
            posx = nx, posy = ny - 1;
          break;
        }
        asd += 1, wtf ^= 1;
      }
      wtf = 0;
      nx2 = x, ny2 = y, posx2 = -1, posy2 = -1, asd2 = 1;
      while (1) {
        if (!wtf)
          nx2 -= 1;
        else
          ny2 -= 1;
        if (nx2 < 1 || ny2 < 1) break;
        if (!zt[nx2][ny2]) {
          if (!wtf)
            posx2 = nx2 + 1, posy2 = ny2;
          else
            posx2 = nx2, posy2 = ny2 + 1;
          break;
        }
        asd2 += 1, wtf ^= 1;
      }
      ans -= asd * asd2, ans += 1;
    }
  }
  int main() {
    while (t--) {
      n = read(), m = read(), q = read();
      for (long long i = 1; i <= n; i += 1)
        for (long long j = 1; j <= m; j += 1) {
          zt[i][j] = 1;
          if (i == j)
            ans += 2 * (2 * i - 1) - 1;
          else if (i > j)
            ans += 2 * (2 * j - 1);
          else
            ans += 2 * (2 * i - 1);
        }
      while (q--) {
        x = read(), y = read();
        zt[x][y] ^= 1, add(x, y, zt[x][y]);
        printf("%lld\n", ans);
      }
    }
    return 0;
  }
  