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: Runtime Error)

import sys
def 解()
    iH,iW,iN = [int(_) for _ in input().split()]
    aD = [[int(_) for _ in sLine.split()] for sLine in sys.stdin.readlines()]

    iMax = (iH - 2) * (iW -2)
    #print (iMax)

    dC={}
    for i in range(10):
        dC[i]=0

    #愚直 無理 つらい
    #for i in range(1,iH -1):
    #   for j in range(1,iW-1):
    #       tmp = 0
    #       for a in aD:
    #           if j<= a[1] <=j+2 and i<= a[0] <= i+2:
    #               tmp +=1
    #       dC[tmp] +=1

    #なんというか、面倒くさくなって解法みても
    #面倒くさがらずやれとしか書いてなくてつらい
    dM = {}
    for a in aD:
        y=a[0]
        x=a[1]
        for aP in [(y-2,x-2),(y-2,x-1),(y-2,x),(y-1,x-2),(y-1,x-1),(y-1,x),(y,x-2),(y,x-1),(y,x)]:
            if 0< aP[0]<iH-1 and 0 < aP[1] < iW-1:
                iP = aP[0]*iW + aP[1]
                if iP in dM: #もう最初から足したったらええんや
                    dM[iP] += 1
                else:
                    dM[iP] = 1
    for i in dM:
        dC[dM[i]]+=1

    iAllBM=0
    for i in range(1,10):
        iAllBM+=dC[i]
    dC[0] = iMax -iAllBM #点のないマス0は引き算で出せる

    for i in range(10):
        print(dC[i])
解()