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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <cstring>
#include <functional>
#include <iostream>
#include <iomanip>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <regex>
#include <vector>

#define fix(n)          cout<<fixed<<setprecision(n)
#define rep(i,n)        for (int i = 0; i < (n); ++i)
#define sort(a)         sort((a).begin(), (a).end())
#define uniq(a)         sort(a);(a).erase(unique((a).begin(), (a).end()), (a).end())
#define reverse(a)      reverse((a).begin(), (a).end())
#define ctos(c)         string(1, (c))
#define out(d)          cout << (d)
#define outl(d)         std::cout<<(d)<<"\n"
#define YES()           cout << "YES" << endl
#define NO()            cout << "NO" << endl
#define Yes()           cout << "Yes" << endl
#define No()            cout << "No" << endl
#define ceil(x, y)      ((x + y - 1) / (y))
#define debug(x)        cerr << #x << ": " << (x) << '\n'
#define debug2(x, y)    cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << '\n'
#define debug3(x, y, z) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << ", " << #z << ": " << (z) << '\n'
#define dbg(v)          for (size_t _ = 0; _ < v.size(); ++_){ cerr << #v << "[" << _ << "] : " << v[_] << '\n'; }

using namespace std;
using ll = long long;
using ld = long double;
using P = pair<ll,ll>;

const ll MOD = 1000000007; // 10^9 + 7
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

void solve() {
  int w, h, n; cin >> w >> h >> n;
  int minX = 0, minY = 0, maxX = w, maxY = h;

  rep(i, n) {
    int x, y, a; cin >> x >> y >> a;
    if (a == 1) minX = x;
    if (a == 2) maxX = x;
    if (a == 3) minY = y;
    if (a == 4) maxY = y;
  }

  if (minX < maxX && minY < maxY)
    outl((maxX - minX) * (maxY - minY));
  else
    outl(0);
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  srand((unsigned)time(NULL));
  fix(12);

  solve();
}