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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <numeric>
#include <functional>
using namespace std;

#define Rep(b, e, i) for(int i = b; i <= e; i++)
#define rep(n, i) Rep(0, n-1, i)

typedef long long ll;
typedef pair<int, int> intP;
typedef std::priority_queue<intP, std::vector<intP>, std::greater<intP> > IntPReversePrioQueue; //A->Z

int dx9[9]={0,0,0,1,1,1,-1,-1,-1};
int dy9[9]={1,0,-1,1,0,-1,1,0,-1};
ll ans[10];

void solve(void){
    ll h, w, n;
    scanf("%lld%lld%lld\n", &h, &w, &n);
    IntPReversePrioQueue que;
    rep(n, i){
        ll a, b;
        scanf("%lld%lld\n", &a, &b);
        rep(9, j) {
            ll x = a+dx9[j], y = b+dy9[j];
            if (2 <= x and x <= (h-1) and 2 <= y and y <= (w-1)) que.push(intP(x, y));
        }
    }
    int mulc = 1;
    intP temp;
    while (que.size()) {
        temp = que.top(); que.pop();
        if (temp != que.top() or que.empty()) {
            ans[mulc]++;
            mulc = 1;
        }
        else mulc++;
        //printf("%d %d\n", temp.first, temp.second);
    }
    ans[0] = (h-2)*(w-2);
    Rep(1, 9, i) ans[0] -= ans[i];
    rep(10, i) printf("%lld\n", ans[i]);
}

int main(void){
  solve();
  return 0;
}