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: Time Limit Exceeded)

fun main(args:Array<String>) {
	val(h,w,n)= readLine()!!.split(" ").map {it.toInt()}
	val ab = (1..n).map {readLine()!!.split(" ").map {it.toInt()-1}}
	val map = mutableMapOf<Pair<Int,Int>,Int>()
	ab.forEach {
		for(dy in -1..1)for(dx in -1..1){
			val y=it[0]+dy
			val x=it[1]+dx
			if(1<=y&&y<=h-2 && 1<=x&&x<=w-2){
				if(map.containsKey(Pair(y,x))) {
					map[Pair(y,x)]=map[Pair(y,x)]!!+1
				}else{
					map[Pair(y,x)]=1
				}
			}
		}
	}
	val ans = map.toList().map{it.second}
			.groupBy {it}.mapValues {it.value.size}
	
	println( (h-2).toLong()*(w-2).toLong() - ans.toList().sumBy {it.second})
	for(i in 1..9){
		if(ans.containsKey(i)){
			println(ans[i])
		}else{
			println(0)
		}
	}
}