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 Scala (2.11.7) (judge verdict: Accepted)

import java.io.{BufferedReader, IOException, InputStream, InputStreamReader}
import java.util.StringTokenizer

import scala.collection.mutable
import scala.util.Sorting
import math.{min, max, abs}

object Main {
  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val H = sc.nextInt()
    val W = sc.nextInt()
    val N = sc.nextInt()
    val p = mutable.Map[(Int, Int), Int]().withDefault(_ => 0)

    (0 until N) foreach { _ =>
      val a = sc.nextInt() - 1
      val b = sc.nextInt() - 1
      for {
        i <- -2 to 0
        j <- -2 to 0
        a0 = a + i
        b0 = b + j
        if 0 <= a0 && a0 <= H - 3 && 0 <= b0 && b0 <= W - 3
      } {
        p((a0, b0)) = p((a0, b0)) + 1
      }
    }

    def max = (H - 2).toLong * (W - 2).toLong
    
    val d = Array.ofDim[Long](10)
    p foreach { case (_, j) => d(j) += 1 }
    d(0) = max - d.drop(1).sum
    d.indices map d foreach println
  }

  def main(args: Array[String]): Unit = {
    solve()
  }



  class InputReader(val stream: InputStream) {
    val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    var tokenizer: StringTokenizer = null

    def next: String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next.toInt
    def nextLong(): Long = next.toLong
    def nextChar(): Char = next.charAt(0)
  }

}