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: Accepted)

use proconio::input;
use proconio::marker::*;
use std::collections::HashMap;

pub const ALL_DIRS: [(isize, isize); 8] = [
    // 時計回り
    (-1, 0),  // 上
    (-1, 1),  // 右上
    (0, 1),   // 右
    (1, 1),   // 右下
    (1, 0),   // 下
    (1, -1),  // 左下
    (0, -1),  // 左
    (-1, -1), // 左上
];

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

    let is_ok = |i: usize, j: usize| -> bool { i > 0 && i < h - 1 && j > 0 && j < w - 1 };
    let mut table = HashMap::new();
    for (a, b) in abv {
        let i = a;
        let j = b;
        if is_ok(i, j) {
            *table.entry((i, j)).or_insert(0) += 1;
        }
        for &(di, dj) in &ALL_DIRS {
            let new_i = i as isize + di;
            let new_j = j as isize + dj;
            if new_i < 0 || new_i >= h as isize || new_j < 0 || new_j >= w as isize {
                continue;
            }
            let new_i = new_i as usize;
            let new_j = new_j as usize;
            if is_ok(new_i, new_j) {
                *table.entry((new_i, new_j)).or_insert(0) += 1;
            }
        }
    }
    let all_count = (w - 3 + 1) * (h - 3 + 1);
    let mut counts = vec![0; 10];
    for (_, c) in table {
        counts[c] += 1;
    }
    let zero_count = all_count - counts.iter().skip(1).sum::<usize>();
    counts[0] = zero_count;
    for c in counts {
        println!("{}", c);
    }
}