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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"io"
	"io/ioutil"
	"os"
)

type contest struct {
	in  io.Reader
	out io.Writer
}

func (con *contest) scan(a ...interface{}) (int, error) {
	return fmt.Fscan(con.in, a...)
}
func (con *contest) scanln(a ...interface{}) (int, error) {
	return fmt.Fscanln(con.in, a...)
}
func (con *contest) scanf(f string, a ...interface{}) (int, error) {
	return fmt.Fscanf(con.in, f, a...)
}
func (con *contest) print(a ...interface{}) (int, error) {
	return fmt.Fprint(con.out, a...)
}
func (con *contest) println(a ...interface{}) (int, error) {
	return fmt.Fprintln(con.out, a...)
}
func (con *contest) printf(f string, a ...interface{}) (int, error) {
	return fmt.Fprintf(con.out, f, a...)
}
func main() {
	//in := bufio.NewReader(os.Stdin)
	b, _ := ioutil.ReadAll(os.Stdin)
	in := bytes.NewBuffer(b)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()
	con := &contest{in: in, out: out}
	con.main()
}

type p struct{ r, c int }

func (con *contest) main() error {
	var H, W, N int
	con.scan(&H, &W, &N)
	M := map[p]int{}
	for i := 0; i < N; i++ {
		var a, b int
		con.scan(&a, &b)
		for r := a - 3; r < a; r++ {
			if r < 0 || r > H-3 {
				continue
			}
			for c := b - 3; c < b; c++ {
				if c < 0 || c > W-3 {
					continue
				}
				M[p{r, c}]++
			}
		}
	}
	A := make([]int, 10)
	for _, v := range M {
		A[v]++
	}
	A[0] = (H-2)*(W-2) - len(M)
	for _, a := range A {
		con.println(a)
	}
	return nil
}