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 (1.42.0) (judge verdict: Wrong Answer)

use std::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

fn count(x: i64, y: i64, map: &HashSet<(i64, i64)>) -> usize {
    let mut ans = 0;
    for i in 0..3 {
        for j in 0..3 {
            if map.contains(&(x+i, y+j)) {
                ans += 1;
            }
        }
    }
    ans
}


fn main() {
    let line: Vec<i64> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let h = line[0];
    let w = line[1];
    let n = line[2] as usize;

    let mut map = HashSet::with_capacity(n);
    for i in 0..n {
        let line: Vec<i64> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let a = line[0];
        let b = line[1];
        map.insert((a, b));
    }
    let mut memo = vec![HashSet::new(); 10];
    for &(x, y) in map.iter() {
        for i in -2..3 {
            for j in -2..3 {
                let x = x + i;
                let y = y + j;
                if 1 <= x && x <= h-2 && 1 <= y && y <= w-2 {
                    let c = count(x, y , &map);

                    memo[c].insert((x, y));
                }
            }
        }
    }
    let mut ans = (h-2) * (w-2);
    for i in 0..10 {
        ans -= memo[i].len() as i64;
    }
    println!("{}", ans);

    for i in 1..10 {
        println!("{}", memo[i].len());
    }
}