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: Time Limit Exceeded)

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

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

if N>0:
  rows.append(ab[N-1][0])
  r_b.append(N)

cols=[[ab[j][1] for j in range(r_b[i],r_b[i+1])] for i in range(len(r_b)-1)]

rN=len(cols)


ched_box=[[[[False]*3 for k in range(3)] for j in range((len(cols[i]) if i<rN else 0))] for i in range(3)]
dic_cn=[dict(zip(cols[i],list(range(len(cols[i]))))) if i<rN else {} for i in range(3)]
area_n=[0]*9

for rn in range(rN):
  cN=len(cols[rn])
  row=rows[rn]

  if rn!=0:
    ched_box[0]=ched_box[1]
    dic_cn[0]=dic_cn[1]
    ched_box[1]=ched_box[2]
    dic_cn[1]=dic_cn[2]
    if rn<rN-2:
      ched_box[2]=[[[False]*3 for k in range(3)] for j in range(len(cols[rn+2]))]
      dic_cn[2]=dict(zip(cols[rn+2],list(range(len(cols[rn+2])))))

  if (rows[rn+1]==row+1 if rn<rN-1 else False):
    row1=row+1
    if (rows[rn+2]==row+2 if rn<rN-2 else False):
      row2=row+2
    else:
      row2=None
  elif (rows[rn+1]==row+2 if rn<rN-1 else False):
    row1=row+2
    row2=None
  else:
    row1=None
    row2=None
  
  for cn in range(cN):
    col=cols[rn][cn]
       
    for box_row in range(3):
      for box_col in range(3):
        if col-2+box_col<1 or col+box_col>W or row-2+box_row<1 or row+box_row>H:
          ched_box[0][cn][box_row][box_col]=True
    find_rowcol=[]
    find_cn=[]
    find_rowcol_app=find_rowcol.append
    find_cn_app=find_cn.append
    for ch_row in range(row,min(row+3,H+1)):
      if ch_row==row:
        for ch_col in range(col+1,min(col+3,W+1)):
          if ch_col in dic_cn[0]:
            find_rowcol_app([row,ch_col])
            find_cn_app(dic_cn[0][ch_col])
      elif ch_row==row1:
        for ch_col in range(max(col-2,1),min(col+3,W+1)):
          if ch_col in dic_cn[1]:
            find_rowcol_app([row1,ch_col])
            find_cn_app(dic_cn[1][ch_col])
      elif ch_row==row2:
        for ch_col in range(max(col-2,1),min(col+3,W+1)):
          if ch_col in dic_cn[2]:
            find_rowcol_app([row2,ch_col])
            find_cn_app(dic_cn[2][ch_col])
            
    count=[[1]*3 for i in range(3)]
    
    ch_box_row_col=[]
    for box_row in range(0,3):
      for box_col in range(0,3):
        if not ched_box[0][cn][box_row][box_col]:
           ch_box_row_col.append([box_row,box_col])
        
    for i,[find_row,find_col] in enumerate(find_rowcol):
      
      if find_row==row:
        ch_rn=0
        ch_cn=find_cn[i]
      elif find_row==row1:
        ch_rn=1
        ch_cn=find_cn[i]
      elif find_row==row2:
        ch_rn=2
        ch_cn=find_cn[i]
      
      for box_row in range(find_row-row,3):
        for box_col in range(max(find_col-col,0),min(3,3+find_col-col)):
          if not ched_box[0][cn][box_row][box_col]:
            count[box_row][box_col]+=1
            ched_box[ch_rn][ch_cn][box_row-find_row+row][box_col-find_col+col]=True
    for [box_row,box_col] in ch_box_row_col:
      area_n[count[box_row][box_col]-1]+=1



print((W-2)*(H-2)-sum(area_n))
for i in range(9):
  print(area_n[i])