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, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;
use std::collections::HashSet;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let h = scan.read::<i64>();
    let w = scan.read::<i64>();
    let n = scan.read::<usize>();
    let ab = arr(n, |_| (scan.read::<i64>()-1, scan.read::<i64>()-1));
    let ab_set = dup::<_, HashSet<_>>(&ab);
    let mut ans = vec![HashSet::new();10];
    for (y, x) in ab {
        let sy = y-2;
        let sx = x-2;
        for ny in sy..sy + 3 {
            for nx in sx..sx + 3 {
                if ny < 0 || nx < 0 {continue;}
                if ny+2 >= h || nx+2 >= w {continue;}
                let mut cnt = 0;
                for i in ny..ny + 3 {
                    for j in nx..nx + 3 {
                        if ab_set.contains(&(i, j)) {
                            cnt += 1;
                        }
                    }
                }
                ans[cnt].insert((ny, nx));
            }
        }
    }
    let ttl = ans.iter().map(|x| x.len() as i64).sum::<i64>();
    println!("{}", (h-2) * (w-2) - ttl);
    for i in 1..10 {
        println!("{}", ans[i].len());
    }
}

// region template
#[allow(dead_code)]
fn iu(i: isize) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> isize { i as isize }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

#[allow(dead_code)]
fn alt<S, T>(v: Vec<S>) -> T where T: FromIterator<S> {
    v.into_iter().collect::<T>()
}

#[allow(dead_code)]
fn dup<S, T>(v: &[S]) -> T where T: FromIterator<S>, S: Clone {
    v.iter().cloned().collect::<T>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion