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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
  "fmt"
)

func main() {
  var w, h, n int
  fmt.Scan(&w, &h, &n)
  points := make([][]int, w)
  for i := range points{
      points[i] = make([]int, h)
  }
  
  var x, y, a int
  for i := 0; i < n; i++ {
	fmt.Scan(&x, &y, &a)
    switch a {
      case 1:
		for j := x-1; j >= 0; j-- {
          for k := 0; k < h; k++ {
            points[j][k] = 1
          }
        }      	
      case 2:
		for j := x; j < w; j++ {
          for k := 0; k < h; k++ {
            points[j][k] = 1
          }
        }
      case 3:
		for j := 0; j < w; j++ {
          for k := y-1; k >= 0; k-- {
            points[j][k] = 1
          }
        }      	
      case 4:
		for j := 0; j < w; j++ {
          for k := y; k < h; k++ {
            points[j][k] = 1
          }
        }
    }
  }

  ans := 0
  
  for i := 0; i < w; i++ {
    for j := 0; j < h; j++ {
      if points[i][j] == 0{
        ans++
      }
    }
  }
  fmt.Printf("%d\n", ans)
}

func abs(a int) int {
  if a < 0 {
    a *= -1
  }
  return a
}