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)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (H, W, N): (i64, i64, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    };
    let (a, b): (Vec<i64>, Vec<i64>) = {
        let (mut a, mut b) = (vec![], vec![]);
        for _ in 0..N {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            a.push(iter.next().unwrap().parse().unwrap());
            b.push(iter.next().unwrap().parse().unwrap());
        }
        (a, b)
    };

    let p = (0..N)
        .map(|i| (a[i], b[i]))
        .collect::<std::collections::HashSet<_>>();
    let mut dp = vec![0; 10];
    for k in 0..N {
        let (y, x) = (a[k], b[k]);
        for u in std::cmp::max(1, y - 2)..(std::cmp::min(H - 2, y) + 1) {
            for l in std::cmp::max(1, x - 2)..(std::cmp::min(W - 2, x) + 1) {
                dp[(u..(u + 3))
                    .map(|i| (l..(l + 3)).filter(|&j| p.contains(&(i, j))).count())
                    .sum::<usize>()] += 1;
            }
        }
    }
    for i in 1..10 {
        dp[i] /= i as i64;
    }
    let ans = (0..10)
        .map(|i| {
            if i == 0 {
                ((H - 2) * (W - 2) - dp.iter().sum::<i64>()).to_string()
            } else {
                dp[i].to_string()
            }
        })
        .collect::<Vec<_>>()
        .join("\n");

    println!("{}", ans);
}