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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
const long long INF = LLONG_MAX / 2;
const long long MOD = 1000000007;
const long double PI = 3.1415926;
#define FOR(i,r,n) for(ll i = (ll)(r); i < (ll)(n); i++)
#define REP(i,n) FOR(i,0,n)
#define ll long long int
#define ALL(x) x.begin(),x.end()
using namespace std;
ll ans = 0, sum = 0, n, k, counter = 0, w, h;
string s;
vector<ll> v;
vector < pair<ll, ll > > vp;
vector<vector<ll> > vv(50, vector<ll>(50, INF));
vector<string> vs;
vector<string> vss;
vector<char> vc;
vector<ll> vi;
vector<ll> vii;
vector<ll> viii;
 
/*--------------------template--------------------*/
 
int main() {
	cin >> k >> h >> n;
	vi.push_back(k);
	viii.push_back(h);
	v.push_back(sum);
	vii.push_back(sum);
	REP(i, n) {
		ll a, b, c;
		cin >> a >> b >> c;
		if (c == 1) {
			v.push_back(a);
		}
		else if (c == 2) {
			vi.push_back(a);
		}
		else if (c == 3) {
			vii.push_back(b);
		}
		else if (c == 4) {
			viii.push_back(b);
		}
	}
	sort(ALL(v));
	sort(ALL(vi));
	sort(ALL(vii));
	sort(ALL(viii));
	//ans = (vi.front() - v.back())*(viii.front() - vii.back());
        ans=(vi[0]-v[v.size()-1])*(viii[0]-vii[vii.size()-1]);
	cout << ans << endl;
}