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: # E. Staircases
  
  from sys import stdin, stdout
  input = stdin.readline
  print = stdout.write
  
  n, m, q = list(map(int, input().split()))
   
  matrix = [[[0, 0] for i in range(m)] for j in range(n)]
  free = [[True for i in range(m)] for j in range(n)]
   
  ans = 0
   
  for i in range(n):
      for j in range(m):
          if i > 0: matrix[i][j][1] += matrix[i-1][j][0]
          if j > 0: matrix[i][j][0] += matrix[i][j-1][1]
          
          matrix[i][j][0] += 1
          matrix[i][j][1] += 1
          
          ans += matrix[i][j][0]+matrix[i][j][1]-1
          
  for _ in range(q):
      x, y = list(map(int, input().split()))
   
      x -= 1
      y -= 1
      
      count_right = 0
      
      act_x = x
      act_y = y+1
      
      right = True
      
      while act_x < n and act_y < m and free[act_x][act_y]:
          count_right += 1
          
          if right:
              act_x += 1
          else: act_y += 1
          
          right = not right
          
      count_down = 0
      
      act_x = x+1
      act_y = y
      
      right = False
      
      while act_x < n and act_y < m and free[act_x][act_y]:
          count_down += 1
          
          if right:
              act_x += 1
          else: act_y += 1
          
          right = not right
          
      count_left = 0
      
      act_x = x
      act_y = y-1
      
      left = True
      
      while act_x >= 0 and act_y >= 0 and free[act_x][act_y]:
          count_left += 1
          
          if left:
              act_x -= 1
          else: act_y -= 1
          
          left = not left
          
      count_up = 0
      
      act_x = x-1
      act_y = y
      
      left = False
      
      while act_x >= 0 and act_y >= 0 and free[act_x][act_y]:
          count_up += 1
          
          if left:
              act_x -= 1
          else: act_y -= 1
          
          left = not left
          
      count_stairs = 0
      
      count_stairs += (count_up+1)*(count_right+1)
      count_stairs += (count_down+1)*(count_left+1)
          
      count_stairs -= 1
      
      if free[x][y]:
          ans -= count_stairs
      else:
          ans += count_stairs
          
      free[x][y] = not free[x][y]
          
      print(str(ans)+"\n")