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: Wrong Answer)

"use strict";
    
const main = arg => {
  // とりあえず切り分け
  let Nums = arg.split("\n");
  // 1行目だけ特別なので取り出す
  let baseInfo = Nums.shift(0);
  let W = baseInfo.split(" ")[0]*1;
  let H = baseInfo.split(" ")[1]*1;
  // 各要素ごとの配列を作る
  let xMin = new Set();
  let xMax = new Set();
  let yMin = new Set();
  let yMax = new Set();
  // そこからケース分でより分ける;
  Nums.forEach(arr=>{
	let m = arr.split(" ")[2]*1;
    // 各要素を切り出して配列を作成
    switch(m){
      case 1:
		xMin.add(arr.split(" ")[0]);
        break;
      case 2:
		xMax.add(arr.split(" ")[0]);
        break;
      case 3:
		yMin.add(arr.split(" ")[1]);
        break;
      case 4:
		yMax.add(arr.split(" ")[1]);
        break;
    }
  })
  // それぞれの配列でsortかけて必要な値を出す
  let xMinNum = xMin.size !== 0? Math.min(...xMin): 0;
  let xMaxNum = xMax.size !== 0? Math.max(...xMax):	0;
  let yMinNum = yMin.size !== 0? Math.min(...yMin): 0;
  let yMaxNum = yMax.size !== 0? Math.max(...yMax): 0;
  
  let xIsOver = xMinNum > xMaxNum;
  let yIsOver = yMinNum > yMaxNum;
  // 面積
  // xとyを端に寄せるようなイメージ
  let newX = xMinNum + (W - xMaxNum);
  let newY = yMinNum + (H - yMaxNum);
	//  let trueX = W - (xMinNum+xMaxNum);
	//  let trueY = H - (yMinNum+yMaxNum);
  let alea = (xIsOver || yIsOver) ? 0 : W*H - newX*H - newY*W + newX*newY;
  console.log(alea);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));