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)

import java.util.*

fun main(args:Array<String>){
    solve()
}

fun solve(){
    val (h,w,n) = readints()
    val m = HashMap<Pair<Int,Int>,Int>()
    fun inside(a : Int, b : Int) : Boolean{
        return (a <= h && b <= w - 2 && a >= 3 && b >= 1)
    }
    repeat(n){
        val (a,b) = readints()
        for(i in 0 .. 2) {
            for (j in -2..0) {
                if(!inside(a + i, b + j)) continue
                if (m[Pair(a + i, b + j)] == null) {
                    m[Pair(a + i, b + j)] = 1
                } else {
                    m[Pair(a + i, b + j)] = m[Pair(a + i, b + j)]?.plus(1)!!
                }
            }
        }
    }
    var sum = 0L
    val ans = LongArray(10)
    m.forEach{
        ans[it.value]++
        sum++
    }
    ans[0] = (h.toLong() - 2) * (w.toLong() - 2) - sum
    for(i in 0 .. 9){
        println(ans[i])
    }
}

fun read() = readLine()!!
fun reads() = readLine()!!.split(" ")
fun readint() = readLine()!!.toInt()
fun readints() = readLine()!!.split(" ").map{it.toInt()}
fun readlong() = readLine()!!.toLong()
fun readlongs() = readLine()!!.split(" ").map{it.toLong()}