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 LuaJIT (2.0.4) (judge verdict: Accepted)

local h, w, n = io.read("*n", "*n", "*n")
local t = {}

local function add(i_h, i_w)
  if not t[i_h] then t[i_h] = {} end
  local v = t[i_h][i_w]
  if v then t[i_h][i_w] = v + 1 else t[i_h][i_w] = 1 end
end

local function subtask(ah, bw)
  if 3 <= bw then add(ah, bw - 2) end
  if 2 <= bw and bw < w then add(ah, bw - 1) end
  if bw < w - 1 then add(ah, bw) end
end

for i = 1, n do
  local ah, bw = io.read("*n", "*n")
  if 3 <= ah then subtask(ah - 2, bw) end
  if 2 <= ah and ah  < h then subtask(ah - 1, bw) end
  if ah < h - 1 then subtask(ah, bw) end
end

local sum = 0
local tbl = {}
for i = 1, 9 do tbl[i] = 0 end
for k, v in pairs(t) do
  for k2, v2 in pairs(v) do
    tbl[v2] = tbl[v2] + 1
    sum = sum + 1
  end
end
local rem = (h - 2LL) * (w - 2LL) - sum
local str = tostring(rem):gsub("LL", "")
print(str)
for i = 1, 9 do print(tbl[i]) end