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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

#define MAX_N   100000

long long result[10];

struct Node {
    int val, x, y, key;
    struct Node *lch, *rch;
};
typedef struct Node node;

node *modify (node *p, int new_x, int new_y, int new_key){
    if(p == NULL){
        node *q = (node*)malloc(sizeof(node));
        q->val = 1;
        q->x = new_x; q->y = new_y;
        q->key = new_key;
        q->lch = q->rch = NULL;
        return q;
    }
    else if (p->key == new_key){
        p->val++;
        return p;
    }
    else {
        if (new_key < p->key) p->lch = modify(p->lch, new_x, new_y, new_key);
        else p->rch = modify(p->rch, new_x, new_y, new_key);
        return p;
    }
}

void answer(node *p){
    if (p != NULL){
        answer(p->lch);
        result[p->val]++;
        result[0]--;
        answer(p->rch);
    }
}

void release(node *p){
    if (p != NULL){
        release(p->lch);
        free(p);
        release(p->rch);
    }
}

void display(node *p){
    if (p != NULL){
        display(p->lch);
        printf("%d  (%d, %d)  %d\n", p->val, p->x, p->y, p->key);
        display(p->rch);
    }
}

int main(){
    int n, i, j, H, W, N, a[MAX_N], b[MAX_N];
    long long key;
    node *root = NULL;
    
    scanf("%d %d %d", &H, &W, &N);
    for (n=0; n<N; n++) scanf("%*c%d %d", &a[n], &b[n]);
    
    result[0] = (long long)(H-2)*(W-2);
    for (n=0; n<N; n++){
        for (i=-1; i<=1; i++){
            if (a[n]-1+i<1 || H-2<a[n]-1+i) continue;
            for (j=-1; j<=1; j++){
                if (b[n]-1+j<1 || W-2<b[n]-1+j) continue;
                key = (long long)(a[n]-1+i)*(W-1)+b[n]-1+j;
                root = modify(root, a[n]-1+i, b[n]-1+j, key);
            }
        }
    }
    answer(root);
    for (i=0; i<10; i++){
        printf("%lld\n", result[i]);
    }
    release(root);
    return 0;
}