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: Accepted)

#include "bits/stdc++.h"
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define ALL(x) (x).begin(), (x).end()     //昇順
#define RALL(x) (x).rbegin(), (x).rend()  // 降順
#define pri(x) cout << (x) << "\n"
#define pri2(x, y) cout << (x) << " " << (y) << "\n"
#define pri3(x, y, z) cout << (x) << " " << (y) << " " << (z) << "\n"
const long long mod = 1e9 + 7;
typedef long long ll;
typedef priority_queue<int> PQ;
typedef vector<long long> VL;
typedef vector<bool> VB;
typedef vector<int> VI;  // VI a(n);
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<char> VC;
typedef vector<VS> VSS;
typedef vector<VC> VCC;
typedef vector<VI> VII;  // VII a(n,vector<int>(m)) n * m
typedef vector<VL> VLL;
typedef pair<int, int> PII;
typedef map<int, int> MP;  // MP a;
typedef vector<pair<ll, ll>> PS;

template <class T, class U> bool chmax(T &a, U b) { if (a <= b) {a = b; return 1;} return 0; }
template <class T, class U>  bool chmin(T &a, U b) { if (a > b) { a = b; return 1; } return 0; }
template <typename T>  ostream &operator<<(ostream &os, vector<T> &v) { os << "{"; rep(i, (int)v.size()) { os << v[i] << (i < v.size() - 1 ? ", " : ""); } os << "}"; return os; }

// g++ -std=c++11 prac.cpp
// operator << (cout,a);
// chmin(min,a)

int main() {
    ll z=0,n,h,m,ans=0,sum=0,k,w,Max=-1,Min=1e9+1;
    bool ok = true;
    string s,t,u;
    cin >> w >> h >> n;
    VI a(n), x(n), y(n);
    rep(i, n) cin >> x[i] >> y[i] >> a[i];
    ll nh=0, nw=0;

    rep(i,n){
      if(a[i] == 1){
        if(nw < x[i]) 
          nw = x[i];
      }
      if(a[i] == 2){
        if(w > x[i])
          w = x[i];
      }
      if(a[i] == 3){
        if(nh < y[i])
          nh = y[i];
      }
      if(a[i] == 4){
        if(h > y[i])
          h = y[i];
      }
    }

    if ((w < nw) ||  (h < nh))
      pri(0);
    else
      pri((w-nw)*(h-nh));

    return 0;
}