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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#!ruby -E Windows-31J:utf-8

def f_hs a,b
    a*1000000000+b
end
def i_hs k
    return k.div(1000000000),k%1000000000
end

blacks = {} 
well_known = {}
result = [0,0,0,0,0,0,0,0,0,0]

h,w,n = $stdin.gets.chomp.split(/\s+/).map{|str|str.to_i}
#storage
(0...n).each{|ln|
    ia,ib = $stdin.gets.chomp.split(/\s+/).map{|str|str.to_i-1}
    blacks[ f_hs ia,ib ] = true
}

#calc
blacks.each{|k,v|
    ia,ib = i_hs k

    (ia-1..ia+1).each{|ca|
        next if ca+1>=h || ca-1<0
        (ib-1..ib+1).each{|cb|
            next if cb+1>=w || cb-1<0
            next if well_known.has_key? f_hs(ca,cb)
            
            # counts
            cnt = 0
            cnt +=1 if blacks.has_key? f_hs(ca-1,cb-1)
            cnt +=1 if blacks.has_key? f_hs(ca-1,cb)
            cnt +=1 if blacks.has_key? f_hs(ca-1,cb+1)
            cnt +=1 if blacks.has_key? f_hs(ca  ,cb-1)
            cnt +=1 if blacks.has_key? f_hs(ca  ,cb)
            cnt +=1 if blacks.has_key? f_hs(ca  ,cb+1)
            cnt +=1 if blacks.has_key? f_hs(ca+1,cb-1)
            cnt +=1 if blacks.has_key? f_hs(ca+1,cb)
            cnt +=1 if blacks.has_key? f_hs(ca+1,cb+1)
            result[cnt]+=1

            # checker
            well_known[ f_hs ca,cb ] = true
        }
    }
}

#possible all
result[0] = (h-2)*(w-2)
(1..9).each{|i| result[0]-=result[i]}

#output
result.each{|r| puts r}