Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. At first, all cells were painted white.

Snuke painted N of these cells. The i-th ( 1 \leq i \leq N ) cell he painted is the cell at the a_i-th row and b_i-th column.

Compute the following:

For each integer j ( 0 \leq j \leq 9 ), how many subrectangles of size 3×3 of the grid contains exactly j black cells, after Snuke painted N cells?

Constraints

3 \leq H \leq 10^9

3 \leq W \leq 10^9

0 \leq N \leq min(10^5,H×W)

1 \leq a_i \leq H (1 \leq i \leq N)

1 \leq b_i \leq W (1 \leq i \leq N)

(a_i, b_i) \neq (a_j, b_j) (i \neq j)

Input

The input is given from Standard Input in the following format:

H W N
a_1 b_1
:
a_N b_N

Output

Print 10 lines.
The (j+1)-th ( 0 \leq j \leq 9 ) line should contain the number of the subrectangles of size 3×3 of the grid that contains exactly j black cells.

Sample Input 1

4 5 8
1 1
1 4
1 5
2 3
3 1
3 2
3 4
4 4

Sample Output 1

0
0
0
2
4
0
0
0
0
0

There are six subrectangles of size 3×3. Two of them contain three black cells each, and the remaining four contain four black cells each.

Sample Input 2

10 10 20
1 1
1 4
1 9
2 5
3 10
4 2
4 7
5 9
6 4
6 6
6 7
7 1
7 3
7 7
8 1
8 5
8 10
9 2
10 4
10 9

Sample Output 2

4
26
22
10
2
0
0
0
0
0

Sample Input 3

1000000000 1000000000 0

Sample Output 3

999999996000000004
0
0
0
0
0
0
0
0
0

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

H,W,N=map(int,input().split())
ab=[list(map(int,input().split())) for i in range(N)]
ab.sort()

r_b=[0]
for i in range(1,N):
  if ab[i][0]!=ab[i-1][0]:
    r_b.append(i)
r_b.append(N)

ab=[ab[r_b[i]:r_b[i+1]] for i in range(len(r_b)-1)]


checked=[[[[False]*3 for k in range(3)]  for j in range(len(ab[i]))] for i in range(min(3,len(ab)))]

area_n=[0 for i in range(1,10)]  
if N is 0:
  ab=[]



for r_n in range(len(ab)//2):
  if r_n!=0:
    checked[0]=checked[1]
    if len(checked)>=3:
      checked[1]=checked[2]
    if r_n<len(ab)-2 and len(checked)==3:
      checked[2]=[[[False]*3 for k in range(3)]  for j in range(len(ab[r_n+2]))]

  row=ab[r_n][0][0]
  
  ch_list_min_add=[0,0]
  
  for c_n in range(len(ab[r_n])):
    col=ab[r_n][c_n][1]

    if row<=2:
      for box_r in range(3-row):
        for box_c in range(3):
          checked[0][c_n][box_r][box_c]=True
    if row>=H-1:
      for box_r in range(H+1-row,3):
        for box_c in range(3):
          checked[0][c_n][box_r][box_c]=True
    if col<=2:
      for box_r in range(3):
        for box_c in range(3-col):
          checked[0][c_n][box_r][box_c]=True
    if col>=W-1:
      for box_r in range(3):
        for box_c in range(W+1-col,3):
          checked[0][c_n][box_r][box_c]=True
    ch_p_rc=[[],[]]
    min_flag=[True,True]
    ch_start_add=ch_list_min_add[:]
    for ch_r in range(row,min(row+3,H+1)):
      if ch_r==row:
        ch_c=min(col+1,W)
        while(ch_c <min(col+min(3,len(ab[r_n])-c_n),W+1)):
          for j in range(min(c_n+1,len(ab[r_n])-1),min(c_n+3,len(ab[r_n]))):
            if ch_c<ab[r_n][j][1]:
              ch_c=ab[r_n][j][1]
              break
            if ab[r_n][j]==[ch_r,ch_c]:
              ch_p_rc[0].append([ch_r,ch_c])
              ch_p_rc[1].append([r_n,j])
              ch_c+=1
              break
            if j==min(c_n+3,len(ab[r_n]))-1:
              ch_c=min(col+3,W+1)
              
      elif ch_r==row+1 and (ab[r_n+1][0][0]==row+1 if r_n<len(ab)-1 else False):
        ch_c=max(col-2,1)
        while(ch_c<min(col+3,W+1)):
          for j in range(ch_start_add[0],len(ab[r_n+1])):
            if ch_c<ab[r_n+1][j][1]:
              ch_c=ab[r_n+1][j][1]
              ch_start_add[0]=j
              if min_flag[0]:
                min_flag[0]=False
                ch_list_min_add[0]=j
              break
            if ab[r_n+1][j]==[ch_r,ch_c]:
              ch_p_rc[0].append([ch_r,ch_c])
              ch_p_rc[1].append([r_n+1,j])
              ch_c+=1
              ch_start_add[0]=min(j+1,len(ab[r_n+1])-1)
              if min_flag[0] and ch_c>col-2:
                min_flag[0]=False
                ch_list_min_add[0]=j
              break
            if j==len(ab[r_n+1])-1:
              ch_c=min(col+3,W+1)
      elif ch_r==row+2 and (ab[r_n+1][0][0]==row+2 if r_n<len(ab)-1 else False):
        ch_c=max(col-2,1)
        while(ch_c<min(col+3,W+1)):
           for j in range(ch_start_add[0],len(ab[r_n+1])):
            if ch_c<ab[r_n+1][j][1]:
              ch_c=ab[r_n+1][j][1]
              ch_start_add[0]=j
              if min_flag[0]:
                min_flag[0]=False
                ch_list_min_add[0]=j
              break
            if ab[r_n+1][j]==[ch_r,ch_c]:
              ch_p_rc[0].append([ch_r,ch_c])
              ch_p_rc[1].append([r_n+1,j])
              ch_c+=1
              ch_start_add[0]=min(j+1,len(ab[r_n+1])-1)
              if min_flag[0] and ch_c>col-2:
                min_flag[0]=False
                ch_list_min_add[0]=j
              break
            if j==len(ab[r_n+1])-1:
              ch_c=min(col+3,W+1)
      elif ch_r==row+2 and (ab[r_n+2][0][0]==row+2 if r_n<len(ab)-2 else False):
        ch_c=max(col-2,1)
        while(ch_c<min(col+3,W+1)):
          for j in range(ch_start_add[1],len(ab[r_n+2])):
            if ch_c<ab[r_n+2][j][1]:
              ch_c=ab[r_n+2][j][1]
              ch_start_add[1]=j
              if min_flag[1]:
                min_flag[1]=False
                ch_list_min_add[1]=j
              break
            if ab[r_n+2][j]==[ch_r,ch_c]:
              ch_p_rc[0].append([ch_r,ch_c])
              ch_p_rc[1].append([r_n+2,j])
              ch_c+=1
              ch_start_add[1]=min(j+1,len(ab[r_n+2])-1)
              if min_flag[1] and ch_c>col-2:
                min_flag[1]=False
                ch_list_min_add[1]=j
              break
            if j==len(ab[r_n+2])-1:
              ch_c=min(col+3,W+1)