output_description: Print the sum of the shortest distances, modulo 10^9+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      H W
      N
      x_1 y_1
      x_2 y_2
      :
      x_N y_N
attempt: print("bandzebo")
  
problem_description: Statement
  
  You are given an H \times W grid. The square at the top-left corner will be
  represented by (0, 0), and the square at the bottom-right corner will be
  represented by (H-1, W-1).
  
  Of those squares, N squares (x_1, y_1), (x_2, y_2), ..., (x_N, y_N) are
  painted black, and the other squares are painted white.
  
  Let the shortest distance between white squares A and B be the minimum number
  of moves required to reach B from A **visiting only white squares** , where
  one can travel to an adjacent square sharing a side (up, down, left or right)
  in one move.
  
  Since there are H × W - N white squares in total, there are _{(H×W-N)}C_2 ways
  to choose two of the white squares.
  
  For each of these _{(H×W-N)}C_2 ways, find the shortest distance between the
  chosen squares, then find the sum of all those distances, modulo 1 000 000
  007=10^9+7.
samples: [{"input": "2 3\n    1\n    1 1", "output": "20\n    \n\nWe have the following grid (`.`: a white square, `#`: a black square).\n\n    \n    \n    ...\n    .#.\n    \n\nLet us assign a letter to each white square as follows:\n\n    \n    \n    ABC\n    D#E\n    \n\nThen, we have:\n\n  * dist(A, B) = 1\n  * dist(A, C) = 2\n  * dist(A, D) = 1\n  * dist(A, E) = 3\n  * dist(B, C) = 1\n  * dist(B, D) = 2\n  * dist(B, E) = 2\n  * dist(C, D) = 3\n  * dist(C, E) = 1\n  * dist(D, E) = 4\n\nwhere dist(A, B) is the shortest distance between A and B. The sum of these\ndistances is 20.\n\n* * *"}, {"input": "2 3\n    1\n    1 2", "output": "16\n    \n\nLet us assign a letter to each white square as follows:\n\n    \n    \n    ABC\n    DE#\n    \n\nThen, we have:\n\n  * dist(A, B) = 1\n  * dist(A, C) = 2\n  * dist(A, D) = 1\n  * dist(A, E) = 2\n  * dist(B, C) = 1\n  * dist(B, D) = 2\n  * dist(B, E) = 1\n  * dist(C, D) = 3\n  * dist(C, E) = 2\n  * dist(D, E) = 1\n\nThe sum of these distances is 16.\n\n* * *"}, {"input": "3 3\n    1\n    1 1", "output": "64\n    \n\n* * *"}, {"input": "4 4\n    4\n    0 1\n    1 1\n    2 1\n    2 2", "output": "268\n    \n\n* * *"}, {"input": "1000000 1000000\n    1\n    0 0", "output": "333211937"}]