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: import sys
  from sys import stdin
  
  def calc(l):
      assert l >= 0
      return l * (l-1) // 2
  
  n,m,q = map(int,stdin.readline().split())
  
  xy = []
  
  """
  cf = [ {} for i in range(2100) ]
  cinds = []
  
  #sides
  for i in range(n):
      j = -1
      diff = (i - 1) - j
      s = i + j
      cf[diff][s] = 1
  
  for i in range(n):
      j = m
      diff = i - j
      s = i + j
      cf[diff][s] = 1
  
  for j in range(m):
      i = -1
      diff = i - j
      s = i + j
      cf[diff][s] = 1
  
  for j in range(m):
      i = n
      diff = (i-1) - j
      s = i + j
      cf[diff][s] = 1
  """
  
  color = [[0] * m for i in range(n)]
  freenum = n * m
  
  ans = 0
  maxi = [float("-inf")] * 2002
  mini = [float("inf")] * 2002
  for i in range(n):
      for j in range(m):
  
          #up
          diff = i - j
          s = i + j
          maxi[diff] = max(maxi[diff] , s)
          mini[diff] = min(mini[diff] , s)
  
          #down
          diff = i - 1 - j
          s = i + j
          maxi[diff] = max(maxi[diff] , s)
          mini[diff] = min(mini[diff] , s)
  
  ans = 0
  for i in range(2002):
      if maxi[i] != float("-inf"):
          #print (i,maxi[i],mini[i])
          ans += calc(maxi[i] - mini[i] + 1)
  
  ANS = []
  #print (ans,freenum,file=sys.stderr)
  
  for i in range(q):
  
      x,y = map(int,stdin.readline().split())
      x -= 1
      y -= 1
  
      #typeA
      #xy is up
      xx = x
      yy = y - 1
      cnt = 0
      while xx >= 0 and yy >= 0 and color[xx][yy] == 0:
          if cnt == 0:
              xx -= 1
          else:
              yy -= 1
          cnt ^= 1
      #down
      XX = x + 1
      YY = y
      cnt = 0
      while XX < n and YY < m and color[XX][YY] == 0:
          if cnt == 0:
              YY += 1
          else:
              XX += 1
          cnt ^= 1
  
      sp = xx + yy
      sq = XX + YY
      sa = x + y
  
      if color[x][y] == 0: #not
          ans -= calc(sq-sp-1)
          ans += calc(sa-sp-1) + calc(sq-sa-1)
      else:
          ans += calc(sq-sp-1)
          ans -= calc(sa-sp-1) + calc(sq-sa-1)
  
      #print (sp,sa,sq)
          
  
      #typeB xy is down
      xx = x - 1
      yy = y 
      cnt = 0
      while xx >= 0 and yy >= 0 and color[xx][yy] == 0:
          if cnt == 0:
              yy -= 1
          else:
              xx -= 1
          cnt ^= 1
      #down
      XX = x
      YY = y + 1
      cnt = 0
      while XX < n and YY < m and color[XX][YY] == 0:
          if cnt == 0:
              XX += 1
          else:
              YY += 1
          cnt ^= 1
  
      sp = xx + yy
      sq = XX + YY
      sa = x + y
  
      if color[x][y] == 0: #not
          ans -= calc(sq-sp-1)
          ans += calc(sa-sp-1) + calc(sq-sa-1)
      else:
          ans += calc(sq-sp-1)
          ans -= calc(sa-sp-1) + calc(sq-sa-1)
  
      
      if color[x][y] == 0:
          freenum -= 1
          color[x][y] = 1
      else:
          freenum += 1
          color[x][y] = 0
      ANS.append(ans + freenum)
  
  print ("\n".join(map(str,ANS)))