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>
#ifdef HIRO
#define d(f_, ...) printf((f_), ##__VA_ARGS__)
#else
#define d(f_, ...)
#endif

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector< pair<int, int> > vii;
typedef vector< pair<long, long> > vllll;
typedef queue<int> qi;
typedef queue< pair<int, int> > qp;
#define mp make_pair
#define pi 3.14159265358979323846
#define MAX max_element
#define MIN min_element
#define all(v) v.begin(), v.end()
#define gt(T) greater<T>()
#define sum(v) accumulate(v.begin(), v.end(), 0)
#define uni(v) do{ \
  sort(v.begin(), v.end()); \
  decltype(v)::iterator result = unique(v.begin(), v.end()); \
  v.erase(result, v.end()); \
}while(0)
#define fi(init, n) for(int i = init; i < n; ++i)
#define fj(init, n) for(int j = init; j < n; ++j)
#define fk(init, n) for(int k = init; k < n; ++k)
#define zero(x) memset(x, 0, sizeof(x))
#define negative(x) memset(x, ~0, sizeof(x))
#define bitsum(x) __builtin_popcount(x)
const ll MOD = 1e9 + 7;
const int INF = 1e9;
const int di[] = { 0, 1, 0, -1 };
const int dj[] = { 1, 0, -1, 0 };

template<typename T>
T gcd(T a, T b) {
	return b ? gcd(b, a % b) : a;
}
template<typename T>
T lcm(T a, T b) {
	return a * b / gcd(a, b);
}
template<typename T>
int finder(vector<T> vec, T number) {
	auto itr = find(vec.begin(), vec.end(), number);
	size_t index = distance(vec.begin(), itr);
	if (index != vec.size()) return 1;
	else return 0;
}
ll frac(ll n){
	if (n == 0) return 1;
	return (n * frac(n - 1)) % MOD;
}
template<class T> inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template<class T> inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

int main(int argc, char** argv) {
#ifdef HIRO
  string quiz(argv[1]);
  string id(argv[2]);
  string filename("input/" + quiz + "/" + id + ".txt");
  ifstream fin(filename);
  if (fin.peek() == ifstream::traits_type::eof()) {
    cout << "No input.";
    return 0;
  }
  ifstream cin(filename);
  std::cin.rdbuf(cin.rdbuf());
#endif
  int ans = 0, w, h, n, x, y, a;
  cin >> w >> h >> n;
  int arr[w][h];
  fi(0, w)
    fj(0, h)
      arr[i][j] = 1;
  
  fi(0, n) {
    cin >> x >> y >> a;
    switch(a) {
      case 1:
        fi(0, x)
          fj(0, h)
            arr[i][j] = 0;
        break;
      case 2:
        fi(x, w)
          fj(0, h)
            arr[i][j] = 0;
        break;
      case 3:
        fi(0, w)
          fj(0, y)
            arr[i][j] = 0;
        break;
      case 4:
        fi(0, w)
          fj(y, h)
            arr[i][j] = 0;
        break;
    }
  }
  fi(0, w)
    fj(0, h)
      ans += arr[i][j];
  cout << ans << endl;
  return 0;
}