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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>

long long x[900000][2];

int l(long long x1, long long x2, long long y1, long long y2){
    if(x1 == y1){
        return x2 < y2;
    }else{
        return x1 < y1;
    }
}

void func(long long s, long long t){
    long long c[2];
    long long i = s, j = t;

    c[0] = x[s][0];
    c[1] = x[s][1];

    if(s < t){
        while(1){
            while(l(x[i][0], x[i][1], c[0], c[1])){
                i++;
            }
            while(l(c[0], c[1], x[j][0], x[j][1])){
                j--;
            }
            if(i >= j){
                break;
            }
            x[i][0] ^= x[j][0] ^= x[i][0] ^= x[j][0];
            x[i][1] ^= x[j][1] ^= x[i][1] ^= x[j][1];
            i++;
            j--;
        }
        func(s, i-1);
        func(j+1, t);
    }
}

int main(void){

    long long H, W, N;

    scanf("%lld%lld%lld", &H, &W, &N);

    long long a[N], b[N];
    long long a2, b2;
    long long n2 = 0;

    for(long long i = 0; i < N; i++){
        scanf("%lld%lld", &a[i], &b[i]);
        for(long long j = 0; j < 3; j++){
            for(long long k = 0; k < 3; k++){
                a2 = a[i] - j;
                b2 = b[i] - k;
                if(a2 > 0 && a2 < H - 1 && b2 > 0 && b2 < W - 1){
                    x[n2][0] = b2;
                    x[n2][1] = a2;
                    n2++;
                }
            }
        }
    }

    long long d[2], z[10];

    for(long long i = 0; i < 10; i++){
        z[i] = 0;
    }

    func(0, n2-1);

    d[0] = x[0][0];
    d[1] = x[0][1];

    long long m = 0;

    for(long long i = 1; i < n2; i++){
        m++;
        if(x[i-1][0] != x[i][0] || x[i-1][1] != x[i][1]){
            z[m]++;
            m = 0;
        }
    }

    if(n2){
        z[m+1]++;
    }
    z[0] = (H-2)*(W-2);

    for(long long i = 1; i < 10; i++){
        z[0] -= z[i];
    }

    for(long long i = 0; i < 10; i++){
        printf("%lld\n", z[i]);
    }

    return 0;
}