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::collections::HashMap;

fn read1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

fn main() {
    let hwn = readn::<usize>(" ");
    let h = hwn[0];
    let w = hwn[1];
    let n = hwn[2];
    
    let mut dict = HashMap::new();

    for _ in 0..n {
        let ab = readn::<usize>(" ");
        let a = ab[0] - 1;
        let b = ab[1] - 1;
        for j in 0..3 {
            if a + j < 2 || a + j >= h { continue; }
            let y = a + j - 2;
            for k in 0..3 {
                if b + k < 2 || b + k >= w { continue; }
                let x = b + k - 2;
                let count = dict.entry((y, x)).or_insert(0);
                *count += 1;
            }
        }
    }

    let mut cnt = vec![0usize; 10];

    for (_, &v) in dict.iter() {
        cnt[v] += 1;
    }

    let zero = (h - 2) * (w - 2) - cnt.iter().sum::<usize>();
    let mut ans = zero.to_string() + "\n";
    for i in 1..10 {
        ans = ans + &(cnt[i].to_string()) + "\n";
    }

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