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: Runtime Error)

package main
import (
	"fmt"
	"bufio"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func readStr() []int {
	sc.Scan()
	tmp := []int{}
	for _, n := range strings.Split(sc.Text(), " ") {
		i, _ := strconv.Atoi(n)
		tmp = append(tmp, i)
	}
	return tmp
}

func main() {
	hwn := readStr()

	points := [][]int{}
	rec := make([][]int, hwn[0])
	for k := range rec {
		rec[k] = make([]int, hwn[1])
	}

	for i := 0; i < hwn[2]; i++ {
		tmp := readStr()
		rec[tmp[0]-1][tmp[1]-1] = 1
		points = append(points, tmp)
	}

	counter := [10]int{}
	for n := 0; n <= hwn[0] - 3; n++ {
		for i := 0; i <= hwn[1] - 3; i++ {
			tmp := 0
			for j := 0; j < 3; j++ {
				for _, r := range rec[j+n][i:i+3] {
					tmp += r
				}
			}
			counter[tmp] += 1
		}
	}

	for _, v := range counter {
		fmt.Println(v)
	}
}