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 (1.3.71) (judge verdict: Time Limit Exceeded)


data class Coordinate(val x: Int, val y: Int) {
    operator fun plus(that: Coordinate): Coordinate {
        return Coordinate(x + that.x, y + that.y)
    }
    companion object {
        val neighbors = (-1 .. 1).flatMap{x -> (-1 .. 1).map{y -> Coordinate(x, y)}}
    }
}

fun main() {
    val (height, width, n) = readLine()!!.trim().split(' ').map(String::toInt)
    val map = mutableMapOf<Coordinate, Int>().withDefault { 0 }
    repeat(n) {
        val (x, y) = readLine()!!.trim().split(' ').map(String::toInt)
        for (next in Coordinate.neighbors.map(Coordinate(x, y)::plus)) if (next.x in 2 until height && next.y in 2 until width) {
            map[next] = map.getOrPut(next){0} + 1
        }
    }
    val result = LongArray(10){0L}.also{it[0] = (height - 2L) * (width - 2L)}
    for (value in map.values) {
        result[value]++
        result[0]--
    }
    println(result.joinToString("\n"))
}