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::stdin;
use std::str::FromStr;
use std::collections::HashSet;
use std::cmp::max;
use std::cmp::min;

fn main(){
    let (h, w, n): (i64, i64, i64) = get_triple();
    let mut abs: Vec<(i64, i64)> = Vec::new();
    for _ in 0..n {
        abs.push(get_pair());
    }

    let mut blacks = HashSet::new();
    let mut visited = HashSet::new();

    for &(a, b) in &abs {
      blacks.insert((a, b));
    }

    let mut anss = vec![0;10];

    for &(u, v) in &blacks {
        for s in max(2, u-1)..min(h, u+2) {
            for t in max(2, v-1)..min(w, v+2) {
                if visited.contains(&(s, t)) { continue; }
                visited.insert((s, t));

                let mut b = 0;
                for x in s-1..s+2 {
                    for y in t-1..t+2 {
                        if blacks.contains(&(x, y)) {
                            b += 1;
                        }
                    }
                }
                anss[b as usize] += 1;
            }
        }
    }

    anss[0] = (h-2) * (w - 2);
    anss[0] -= anss[1..10].iter().fold(0, |acc, x| acc + x);
    for ans in &anss {
        println!("{}", ans);
    }
}


#[allow(dead_code)]
fn get_line() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn get_vec<T: std::str::FromStr>() -> Vec<T> {
    let line = get_line();
    line.split_whitespace().filter_map(|x| x.parse().ok()).collect()
}

#[allow(dead_code)]
fn get_one<T: FromStr + Copy>() -> T {
    let v = get_vec();
    v[0]
}

#[allow(dead_code)]
fn get_pair<T: FromStr + Copy>() -> (T, T) {
    let v = get_vec();
    (v[0], v[1])
}

#[allow(dead_code)]
fn get_triple<T: FromStr + Copy>() -> (T, T, T) {
    let v = get_vec();
    (v[0], v[1], v[2])
}

#[allow(dead_code)]
fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}