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 (1.15.1) (judge verdict: Accepted)

use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let h: usize = itr.next().unwrap().parse().unwrap();
    let w: usize = itr.next().unwrap().parse().unwrap();
    let n: usize = itr.next().unwrap().parse().unwrap();

    let dx: Vec<isize> = [0, 0, -1, 0, 1, -1, 1, -1, 1].to_vec();
    let dy: Vec<isize> = [0, 1, 0, -1, 0, -1, 1, 1, -1].to_vec();
    let mut pos = std::collections::HashMap::new();

    for _ in 0..n {
        let b: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        let a: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        for i in 0..9 {
            let nx = a as isize + dx[i];
            let ny = b as isize + dy[i];
            if 0 < nx && nx < w as isize - 1 && 0 < ny && ny < h as isize - 1 {
                let p = pos.entry((ny, nx)).or_insert(0);
                *p += 1;
            }
        }
    }

    let mut ans = vec![0; 10];
    let mut sum = (h - 2) * (w - 2);
    for (_, v) in pos {
        ans[v] += 1;
        sum -= 1;
    }
    ans[0] = sum;
    let mut out = Vec::new();
    for i in 0..10 {
        writeln!(out, "{}", ans[i]).ok();
    }
    stdout().write_all(&out).unwrap();
}