Problem:
Score : 200 points

Problem Statement

There is a rectangle in the xy-plane, with its lower left corner at (0, 0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.

Snuke plotted N points into the rectangle. The coordinate of the i-th (1 ≦ i ≦ N) point was (x_i, y_i).

Then, he created an integer sequence a of length N, and for each 1 ≦ i ≦ N, he painted some region within the rectangle black, as follows:

If a_i = 1, he painted the region satisfying x < x_i within the rectangle.

If a_i = 2, he painted the region satisfying x > x_i within the rectangle.

If a_i = 3, he painted the region satisfying y < y_i within the rectangle.

If a_i = 4, he painted the region satisfying y > y_i within the rectangle.

Find the area of the white region within the rectangle after he finished painting.

Constraints

1 ≦ W, H ≦ 100

1 ≦ N ≦ 100

0 ≦ x_i ≦ W (1 ≦ i ≦ N)

0 ≦ y_i ≦ H (1 ≦ i ≦ N)

W, H (21:32, added), x_i and y_i are integers.

a_i (1 ≦ i ≦ N) is 1, 2, 3 or 4.

Input

The input is given from Standard Input in the following format:

W H N
x_1 y_1 a_1
x_2 y_2 a_2
:
x_N y_N a_N

Output

Print the area of the white region within the rectangle after Snuke finished painting.

Sample Input 1

5 4 2
2 1 1
3 3 4

Sample Output 1

9

The figure below shows the rectangle before Snuke starts painting.

First, as (x_1, y_1) = (2, 1) and a_1 = 1, he paints the region satisfying x < 2 within the rectangle:

Then, as (x_2, y_2) = (3, 3) and a_2 = 4, he paints the region satisfying y > 3 within the rectangle:

Now, the area of the white region within the rectangle is 9.

Sample Input 2

5 4 3
2 1 1
3 3 4
1 4 2

Sample Output 2

0

It is possible that the whole region within the rectangle is painted black.

Sample Input 3

10 10 5
1 6 1
4 1 3
6 9 4
9 4 2
3 1 3

Sample Output 3

64

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

program Project1;

{$APPTYPE CONSOLE}

uses
  SysUtils;
var
  w,h,n,ni,i,j,a,x,y,sum:Integer;
  xy:array of array of Integer;
begin
  try
    { TODO -oUser -cConsole Main : ぬりえ }
    Read(w);
    Read(h);
    Readln(n);

    SetLength(xy,h,w);

    for i := 0 to h - 1 do
      for j := 0 to w - 1 do
        xy[i,j]:=0;

    for ni := 0 to n-1 do begin
      Read(x);
      Read(y);
      Readln(a);
      case a of
        1:begin
          for i := 0 to h - 1 do
            for j := 0 to x - 1 do
              xy[i,j]:=1;
        end;
        2:begin
          for i := 0 to h-1 do
            for j := x to w - 1 do
              xy[i,j]:=1;
        end;
        3:begin
          for i := 0 to y - 1 do
            for j := 0 to w - 1 do
              xy[i,j]:=1;
        end;
        4:begin
          for i := y to h - 1 do
            for j := 0 to w - 1 do
              xy[i,j]:=1;
        end;
      end;
    end;

    sum:=0;
    for i := 0 to h - 1 do
      for j := 0 to w - 1 do
        sum:=sum+(xy[i,j]xor 1 xor 0);

    Writeln(sum);
    Readln;
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
end.