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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <set>
#include <algorithm>

#define mp make_pair
#define pb push_back
#define ppb pop_back

using namespace std;

typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef vector<ll> vl;
typedef vector<pll> vpl;
typedef vector<vl> vvl;

ll doOp(string op);

#define forn(i, n) for (int i = 0; i < (int)(n); ++i)
#define fors(i, n, s) for (int i = 0; i < (int)(n); i += s)
#define forn1(i, n) for (int i = 1; i <= (int)(n); ++i)
#define forn11(i, n) for (int i = 1; i < (int)(n); ++i)
#define forr(i, n) for (int i = (int)(n) - 1; i >= 0; --i)

#define prOk(ok) cout << ((ok) ? "Yes" : "No")
#define in insert
#define rem remove

#define linf ((ll) 1e9)
#define inf ((int) 1e5)

int main()
{

	ll w, h, n;

	cin >> w >> h >> n;

	bool **a = new bool*[w];
	forn(i, w)
		a[i] = new bool[h];

	forn(i, n)
	{
		ll x, y;
		cin >> x >> y;
		a[x - 1][y - 1] = true;
	}

	ll res[10] = {};

	forn(x, w - 2)
	{
		forn(y, h - 2)
		{
			int r = 0;
			forn(i, 3)
			{
				forn(j, 3)
					r += (int) a[x+i][y+j];
			}
			res[r]++;
		}
	}

	forn(i, 10)
		cout << res[i] << endl;

	return 0;
}