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: Time Limit Exceeded)

package main

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



var sc = bufio.NewScanner(os.Stdin)

func nextLine() string {
    sc.Scan()
    return sc.Text()
}

func main() {
    line := nextLine()
    cols := strings.Fields(line)
    fieldH, _ := strconv.Atoi(cols[0])
    fieldW, _ := strconv.Atoi(cols[1])
    blackNum, _ := strconv.Atoi(cols[2])

    field := make([][]bool, fieldH)
    for i := 0; i < fieldH; i++ {
        field[i] = make([]bool, fieldW)
    }

    for i := 0; i < blackNum; i++ {
        line = nextLine()
        cols = strings.Fields(line)
        lineNum, _ := strconv.Atoi(cols[0])
        colNum, _ := strconv.Atoi(cols[1])
        field[lineNum - 1][colNum - 1] = true
    }


    for i := 0; i < 10; i ++ {
        answer := 0
        for j := 0; j <= fieldW -3; j++ {
            for k := 0; k <= fieldH -3; k++ {
                // 3*3マスのカウント
                count := 0
                for l := 0; l < 3; l ++ {
                    for m:= 0; m < 3; m++ {
                        if field[k +l][j + m] {
                            count++
                        }
                    }
                }
                if count == i {
                    answer++
                }
            }
        }
        fmt.Println(answer)
    }
}