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";

var input = require("fs").readFileSync("/dev/stdin", "utf8");
var cin = input.split(/ |\n/),
    cid = 0;

function next() {
    return +cin[cid++];
} // number一個取得
function nextstr() {
    return cin[cid++];
} // 文字列一個取得
function nextbig() {
    return BigInt(cin[cid++]);
} // BigInteger一個取得
// 長さnの配列として取得。aは文字列フラグ
function nexts(n, a) {
    return a ? cin.slice(cid, cid += n) : cin.slice(cid, cid += n).map(a => +a);
}
// 長さnのBigInt配列として取得。
function nextsbig(n) {
    return cin.slice(cid, cid += n).map(a => BigInt(a));
}
// w個ずつを組にして長さhの配列。aは文字列フラグ。
function nextm(h, w, a) {
    var r = [],
        i = 0;
    if (a)
        for (; i < h; i++) r.push(cin.slice(cid, cid += w));
    else
        for (; i < h; i++) r.push(cin.slice(cid, cid += w).map(a => +a));
    return r;
}
// 多次元配列。v,a1,a2,a3 なら、3次元。[[値vで長さa3の配列]をa2個並べた配列]をa1個並べた配列。
function xArray(v) {
    var a = arguments,
        l = a.length,
        r = "Array(a[" + --l + "]).fill().map(x=>{return " + v + ";})";
    while (--l) r = "Array(a[" + l + "]).fill().map(x=>" + r + ")";
    return eval(r);
}


console.log(main().toString());

function main() {
    let w = next();
    let h = next();
    let n = next();
    let xya = nextm(n, 3)
    let t1 = [];
    let t2 = [];
    let t3 = [];
    let t4 = [];
    // xyaをaでソート
    // console.log({xya})
    xya.forEach(v => {
        if (v[2] == 1) t1.push(v)
        if (v[2] == 2) t2.push(v)
        if (v[2] == 3) t3.push(v)
        if (v[2] == 4) t4.push(v)
    });
    //console.log(t1,t2,t3,t4)
    t1 = t1.length > 0 ? t1.sort((a, b) => b[0] - a[0])[0][0] : 0
    t2 = t2.length > 0 ? t2.sort((a, b) => a[0] - b[0])[0][0] : w
    t3 = t3.length > 0 ? t3.sort((a, b) => b[1] - a[1])[0][1] : 0
    t4 = t4.length > 0 ? t4.sort((a, b) => a[1] - b[1])[0][1] : h

    //console.log(t1,t2,t3,t4)
    return Math.max(t2 - t1, 0) * Math.max(t4 - t3, 0)
}