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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.HashMap;
import java.util.Objects;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int H = scanner.nextInt();
    int W = scanner.nextInt();
    int N = scanner.nextInt();
    HashMap<Point, Integer> freq = new HashMap<>();
    for (int i = 0; i < N; i++) {
      int x = scanner.nextInt();
      int y = scanner.nextInt();
      for (int j = -1; j <= 1; j++) {
        for (int k = -1; k <= 1; k++) {
          int sx = x + j;
          int sy = y + k;
          if (sx > 1 && sx < H && sy > 1 && sy < W) {
            Point p = new Point(sx, sy);
            freq.put(p, freq.getOrDefault(p, 0) + 1);
          }
        }
      }
    }

    long[] total = new long[10];
    total[0] = (long) (H - 2) * (W - 2) - freq.size();
    for (int f : freq.values()) total[f]++;
    for (long t : total) {
      System.out.println(t);
    }
  }

  private static class Point {
    public final int x;
    public final int y;

    private Point(int x, int y) {
      this.x = x;
      this.y = y;
    }

    @Override public boolean equals(Object o) {
      if (this == o) return true;
      if (o == null || getClass() != o.getClass()) return false;
      Point point = (Point) o;
      return x == point.x &&
          y == point.y;
    }

    @Override public int hashCode() {
      return Objects.hash(x, y);
    }
  }
}