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: Accepted)

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

struct xy_t {
	int32_t x, y;
};

int cmp(const void* asumikana, const void* kitamuraeri) {
	struct xy_t a = *(const struct xy_t*)asumikana, b = *(const struct xy_t*)kitamuraeri;
	if (a.y < b.y) return -1;
	if (a.y > b.y) return 1;
	if (a.x < b.x) return -1;
	return a.x > b.x;
}

int32_t H, W;
int32_t N;
int32_t a[114514], b[114514];

int32_t masuCount = 0;
struct xy_t masu[114514 * 9];


int main(void) {
	int32_t i, dx, dy, start;
	uint64_t seisuCount[10] = {0};
	uint64_t zero;
	if (scanf("%" SCNd32 "%" SCNd32 "%" SCNd32, &H, &W, &N) != 3) return 1;
	for (i = 0; i < N; i++) {
		if (scanf("%" SCNd32 "%" SCNd32, &a[i], &b[i]) != 2) return 1;
		for (dy = -1; dy <= 1; dy++) {
			for (dx = -1; dx <= 1; dx++) {
				int32_t x = b[i] + dx, y = a[i] + dy;
				if (1 < x && x < W && 1 < y && y < H) {
					masu[masuCount].x = x;
					masu[masuCount].y = y;
					masuCount++;
				}
			}
		}
	}
	qsort(masu, masuCount, sizeof(*masu), cmp);
	start = 0;
	zero = (uint64_t)(H - 2) * (uint64_t)(W - 2);
	if (masuCount > 0) {
		for (i = 1; i < masuCount; i++) {
			if (cmp(&masu[i - 1], &masu[i]) != 0) {
				int32_t value = i - start;
				if (value < 10) seisuCount[value]++;
				start = i;
			}
		}
		if (i - start < 10) seisuCount[i - start]++;
	}
	for (i = 1; i <= 9; i++) zero -= seisuCount[i];
	printf("%" PRIu64 "\n", zero);
	for (i = 1; i <= 9; i++) printf("%" PRIu64 "\n", seisuCount[i]);
	return 0;
}