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::BTreeSet;

fn main() {
    let (h, w, n) = {
        let a = getvec::<i64>();
        (a[0], a[1], a[2])
    };
    let mut black = BTreeSet::new();
    let mut cand = BTreeSet::new();
    for _ in 0..n {
        let (y, x) = {
            let a = getvec::<i64>();
            (a[0], a[1])
        };
        black.insert((y, x));
        for i in (y - 2)..(y + 1) {
            for j in (x - 2)..(x + 1) {
                if i > 0 && j > 0 && i < h - 1 && j < w - 1 {
                    cand.insert((i, j));
                }
            }
        }
    }
    let mut ans = [0i64; 10];
    for &p in &cand {
        let (i, j) = p;
        let mut sum : usize = 0;
        for x in j..j + 3 {
            for y in i..i + 3 {
                if black.contains(&(y, x)) {
                    sum = sum + 1;
                }
            }
        }
        ans[sum] += 1;
    }
    ans[0] = (h - 2) * (w - 2);
    for i in 1..10 {
        ans[0] -= ans[i];
    }
    for i in 0..10 {
        println!("{}", ans[i]);
    }
}

fn next_line() -> String {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input).unwrap();
    input
}

#[allow(dead_code)]
fn getnum<T : std::str::FromStr>() -> T {
    let res = next_line();
    let res = res.trim().parse::<T>().ok().unwrap();
    res
}

#[allow(dead_code)]
fn getvec<T : std::str::FromStr>() -> Vec<T> {
    let res = next_line();
    let res : Vec<T> = res.split_whitespace().map(|x| x.parse::<T>().ok().unwrap()).collect();
    return res;
}