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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;



class Program
{
    const int MOD = 1000000007;
    const int INF = 1 << 30;



    static void Main(string[] args)
    {
        Solve();
    }



    static void Solve()
    {
        Scaner sc = new Scaner();
        write wr = new write();
        Math2 mmath = new Math2();
        //ここから



        var x = sc.IntArr;

        long H = x[0];
        long W = x[1];
        long N = x[2];
        var ans = new long[10];

        var d = new Dictionary<KeyValuePair<long, long>, long>();


        for (long i = 0; i < N; ++i)
        {
            var y = sc.LongArr;
            long a = y[0]-1;
            long b = y[1]-1;

            for (long j = 0; j <= 2; ++j)
            {
                for (long k = 0; k <= 2; ++k)
                {
                    long Y=a-j;
                    long X=b-k;
                    KeyValuePair<long, long> ddd = new KeyValuePair<long, long>(X,Y);
                    
                    if (X < 0 || X>=W-2 || Y< 0 || Y>=H-2) continue;
                    if (!d.ContainsKey(ddd))
                    {
                        d.Add(ddd, 0);
                    }
                    d[ddd]++;
                }
            }


        }


        foreach (var i in d)
        {
            ans[i.Value]++;
        }
        ans[0] = (H-2) * (W-2);

        for (int i = 1; i < 10; ++i)
        {
            ans[0] -= ans[i];
        }
        for (int i = 0; i < 10; ++i)
        {
            wr.wri(ans[i]);
        }

    }
}

class PriorityQueue<T>
{
    private readonly List<T> heap;
    private readonly Comparison<T> compare;
    private int size;
    public PriorityQueue() : this(Comparer<T>.Default) {} 
    public PriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) { }
    public PriorityQueue(Comparison<T> comparison) : this(16, comparison) { }
    public PriorityQueue(int capacity, Comparison<T> comparison)
    {
        this.heap = new List<T>(capacity);
        this.compare = comparison;
    }
    public void Enqueue(T item)
    {
        this.heap.Add(item);
        var i = size++;
        while (i > 0)
        {
            var p = (i - 1) >> 1;
            if (compare(this.heap[p], item) <= 0)
                break;
            this.heap[i] = heap[p];
            i = p;
        }
        this.heap[i] = item;

    }
    public T Dequeue()
    {
        var ret = this.heap[0];
        var x = this.heap[--size];
        var i = 0;
        while ((i << 1) + 1 < size)
        {
            var a = (i << 1) + 1;
            var b = (i << 1) + 2;
            if (b < size && compare(heap[b], heap[a]) < 0) a = b;
            if (compare(heap[a], x) >= 0)
                break;
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        heap.RemoveAt(size);
        return ret;
    }
    public T Peek() { return heap[0]; }
    public int Count { get { return size; } }
    public bool Any() { return size > 0; }
}


 class Math2
{
    public long[] Fact;  //Nまでの階乗
    public long[] invFact;  //階乗の逆元

    //Nまでの階乗をセットしておく
    public void FactoricalModSet(long N,long MOD=1000000007)
    {
        Fact = new long[N + 1];
        invFact = new long[N + 1];

        Fact[0] = 1;
        for(long i = 1; i <= N; ++i)
        {
            Fact[i] = Fact[i - 1] * i%MOD;
        }
        invFact[N] = powMOD(Fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invFact[i - 1] = invFact[i] * i%MOD;
        }

    }

    public long nCrMod(long n,long r,long MOD=1000000007)
    {
        return (Fact[n] * invFact[r] % MOD * invFact[n-r]%MOD);
    }

    public long powMOD(long x,long n,long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * x % MOD;
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    static long GCD(long x, long y)
    {
        if (y == 0) return x;
        return GCD(y, x % y);
    }

    static long LCM(long x, long y)
    {
        return x * y / GCD(x, y);
    }
}


class Scaner
{
    public string Str => Console.ReadLine();

    public string[] StrArr => Str.Split(' ');

    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public char[] CharArr => Str.ToArray();
    public long Long1 => LongArr[0];
    public int Int1 => IntArr[0];
    
}



class write
{
    public  void wri<T>(T x)
    {
        Console.WriteLine(x);
    }
}