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)

# AtCoder My Practice
# author: Leonardone @ NEETSDKASU
############################################################
def gs() gets.strip end
def gi() gets.to_i end
def gf() gets.to_f end
def gss() gs.split end
def gis() gss.map(&:to_i) end
def nmapf(n,f) n.times.map{ __send__ f } end
def ngs(n) nmapf n,:gs end
def ngi(n) nmapf n,:gi end
def ngss(n) nmapf n,:gss end
def ngis(n) nmapf n,:gis end
def arr2d(h,w,v=0) h.times.map{[v] * w} end
def for2p(hr,wr,&pr) hr.each{|i|wr.each{|j| yield(i,j)}} end
def nsum(n) n * (n + 1) / 2 end
def vcount(d,r=Hash.new(0)) d.inject(r){|m,e| m[e]+=1;m} end
MV4 = [[0, 1], [1, 0], [0, -1], [-1, 0]]
MV8 = MV4 + [[1, 1], [1, -1], [-1, -1], [-1, 1]]
DV7 = 7 + 10 ** 9
############################################################
 
# 解説読後
# http://arc061.contest.atcoder.jp/data/arc/061/editorial.pdf

H, W, N = gis

mp = Hash.new 0

ngis(N).each do |a, b|
    for2p(-3 .. -1, -3 .. -1) do |dy, dx|
        y, x = a + dy , b + dx
        mp[[y, x]] += 1
    end
end
   
ans = [0] * 10

mp.each do |k, c|
    y, x = k
    next if !(0 ... H - 2).include? y
    next if !(0 ... W - 2).include? x
    ans[c] += 1
end

ans[0] = (H - 2) * (W - 2) - ans.inject(:+)

puts ans * "\n"