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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (h, w, n) = readLine()!!.split(' ').map(String::toLong)
    val abMap = mutableMapOf<Pair<Long, Long>, Boolean>()
    val abList = (1..n).map {
        val (a, b) = readLine()!!.split(' ').map(String::toLong)
//        abMap[Pair(a, b)] = false
        Pair(a, b)
    }


    val total = (h - 2) * (w - 2)
    val ansArray = LongArray(10) { 0 }
    ansArray[0] = total

    for (ab in abList) {
        val (a, b) = ab
        for (dw in -1..1) {
            for (dh in -1..1) {
                if (a + dh - 1 < 1) continue
                if (a + dh + 1 > h) continue
                if (b + dw - 1 < 1) continue
                if (b + dw + 1 > w) continue

                var count = 0
                for (dw2 in -1..1) {
                    for (dh2 in -1..1) {
                        val th = a + dh + dh2
                        val tw = b + dw + dw2
                        if (th == a && tw == b) continue
                        if (abMap[Pair(th, tw)] != null) {
                            count++
                        }

                    }
                }
                ansArray[count]--
                ansArray[count + 1]++
            }
        }
        abMap[Pair(a, b)] = false
    }

    (0..9).forEach { println(ansArray[it]) }
}