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 JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

function Main(input) {
  input=input.split("\n");
　const H=input[0].split(" ")[0]-0;
  const W=input[0].split(" ")[1]-0;
  var answer=new Array(10);
  answer.fill(0);
  answer[0]=(H-2)*(W-2);
  if(input.length===1){
    console.log(answer.join("\n"));
    return;
  }
  var array=new Array(H);
  for(var i=0;i<H;i++){
    array[i]=new Array(W);
    array[i].fill(false);
  }
  var temp;
  var counter;
  for(var i=1;i<input.length;i++){
    temp=input[i].split(" ");
    [0,1].forEach(e=>{
      temp[e]-=1;
    });
    array[temp[0]][temp[1]]=true;
    [-1,0,1].forEach(a=>{
      [-1,0,1].forEach(b=>{
        if(1<=a+temp[0]&&a+temp[0]<H-1&&1<=b+temp[1]&&b+temp[1]<W-1){
          counter=0;
          [-1,0,1].forEach(c=>{
            [-1,0,1].forEach(d=>{
              counter+=array[temp[0]+a+c][temp[1]+b+d]?1:0;
            });
          });
          answer[counter-1]--;
          answer[counter]++;
        }
      });
    });
  }
  console.log(answer.join("\n"));
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));