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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'
const main = arg => {
	const input = arg.trim().split("\n");
	let W = input[0].split(' ').map(num => Number(num))[0]
	let H = input[0].split(' ').map(num => Number(num))[1]
	let Xs = input.slice(1, input.length).map(el => Number(el.split(' ')[0]))
	let Ys = input.slice(1, input.length).map(el => Number(el.split(' ')[1]))
	let As = input.slice(1, input.length).map(el => Number(el.split(' ')[2]))
	let base = {x: 0, y: 0}
	let topRight = {x: W, y: H}
 
	for(let i = 0 ; i < As.length ; i++) {
		let a = As[i]
		switch (a) {
			case 1:
				base.x = Xs[i] > base.x ? Xs[i] : base.x
				break
			case 2:
				topRight.x = Xs[i] < topRight.x ? Xs[i] : topRight.x
				break
			case 3:
				base.y = Ys[i] > base.y ? Ys[i] : base.y
				break
			case 4:
				topRight.y = Ys[i] < topRight.y ? Ys[i] : topRight.y
				break
		}
	}
	const width = topRight.x - base.x
	const height = topRight.y - base.y
	const square = width * height
	if(square < 0 || width < 0 || height < 0) {
		console.log(0)
	} else {
		console.log(square)
	}
}   
main(require('fs').readFileSync('/dev/stdin', 'utf8'));