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(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<i64>();
    let (h, w, n) = (v[0], v[1], v[2]);
    let mut grids = HashSet::new();
    for _ in 0..n {
        let v = read_vec::<i64>();
        grids.insert((v[0] - 1, v[1] - 1));
    }
    let mut answers = [0; 10];
    for &(y, x) in grids.iter() {
        for y_offset in -2..1 {
            if y + y_offset < 0 {
                continue;
            }
            if y + y_offset + 2 > h - 1 {
                continue;
            }
            for x_offset in -2..1 {
                if x + x_offset < 0 {
                    continue;
                }
                if x + x_offset + 2 > w - 1 {
                    continue;
                }
                let x_origin = x + x_offset;
                let y_origin = y + y_offset;
                let mut count = 0;
                for x_search in x_origin..x_origin + 3 {
                    for y_search in y_origin..y_origin + 3 {
                        if grids.contains(&(y_search, x_search)) {
                            count += 1;
                        }
                    }
                }
                answers[count] += 1;
            }
        }
    }
    for i in 1..10 as usize {
        answers[i] /= i as i64;
    }
    answers[0] = (h - 2) * (w - 2) - (1..10).map(|x| answers[x]).sum::<i64>();

    for &ans in answers.iter() {
        println!("{:?}", ans);
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}