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 Rust (1.42.0) (judge verdict: Runtime Error)

#[allow(unused_imports)] use proconio::{input, marker::{Bytes, Chars, Usize1, Isize1}};
#[allow(unused_imports)] use std::cmp::{min, max};

fn main() {
	input! {
		h: usize,
		w: usize,
		n: usize,
		ab: [(Usize1, Usize1); n],
	}

	// 3x3の中の黒の個数
	let mut v = vec![vec![0usize; w-2]; h-2];
	// 0-9のカウント
	let mut ans = [0usize; 10];
	ans[0] = (h-2)*(w-2);

	for i in 0..n {
		// この点が含まれる3x3は最大9つある
		for y in max(0, ab[i].0 as isize -2) as usize..=min(h-2-1, ab[i].0) {
			for x in max(0, ab[i].1 as isize -2) as usize..=min(w-2-1, ab[i].1) {
				ans[v[y][x]] -= 1;
				v[y][x] += 1;
				ans[v[y][x]] += 1;
			}
		}
	}

	for i in 0..10 {
		println!("{}", ans[i]);
	}
}