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) = readIntegers()
    val map = hashMapOf<Point, Int>()
    for (i in 0 until n) {
        val (a, b) = readIntegers()

        if ((a in 2 until h) && (b in 2 until w)) {
            val point = Point(a, b)
            map[point] = map.getOrElse(point) { 0 } + 1
        }

        for (j in -1..1) {
            val row = a + j
            if (!(row in 2 until h)) {
                continue
            }

            for (k in -1..1) {
                val column = b + k
                if (!(column in 2 until w)) {
                    continue
                }

                if (j == 0 && k == 0) {
                    continue
                }

                val tmp = Point(row, column)
                map[tmp] = map.getOrElse(tmp) { 0 } + 1
            }
        }
    }

    val zeroCount = (h - 2).toLong() * (w - 2).toLong() - map.count()
    println(zeroCount)
    for (i in 1..9) {
        println(map.values.count { it == i })
    }
}

fun readStrings() = readLine()!!.split(" ")
fun readIntegers() = readStrings().map(String::toInt)

data class Point(val row: Int, val column: Int)