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>
                using namespace std;
                typedef long long ll;
                #define INPUT()              freopen("input.txt", "r", stdin)
                #define OUTPUT()             freopen("output.txt", "w", stdout)
                #define F                    first
                #define S                    second
            //Templatefunctions
                template<typename T>T gcd(T x, T y) { if (y == 0)return x; else return gcd(y, x%y);}
                template <class T> T euclideanDistance(T x1 , T x2 , T y1 , T y2){return sqrt(( x1 - x2 ) * ( x1 - x2 ) + ( y1 - y2 ) * ( y1 - y2 ));}
                template <class T> T digitSum(T n){T sum = 0;while(n > 0)sum += n % 10,n /= 10;return sum;}
            //datatypes
                typedef long long int ll;
                typedef unsigned long long int ull;
                typedef long double ld;
            //constants
                const double INF = 1e+9;
                const double INFLL = 1e+18;
                const double EPS = 1e-9;
                const double PI = acos(-1);
                const int knightDir[8][2] = {{-2,-1},{-2,1},{-1,2},{1,2},{2,-1},{2,1},{-1,-2},{1,-2}};
                       //const int dx[]={0,0,0,1,1,1,-1,-1,-1};
                       //const int dy[]={-1,0,1,-1,0,1,-1,0,1};
                const int dx[] = {0 , 1 , 0 , -1};
                const int dy[] = {1 , 0 , -1 , 0};
            //helpers
                //#define MOD         1000000007LL
                #define MAX         1000005
                const ll MOD = 998244353;
                int arr[MAX];
            //Global Variables



                int main()
                {
                        int w , h , n;
                        scanf("%d%d%d",&w,&h,&n);
                        int x0 = 0,xn = w , y0 = 0, yn = h;
                        for(int i = 0 ; i < n ;i++)
                        {
                            int x , y , a;
                            scanf("%d%d%d",&x, &y ,&a);

                            if(a == 1)
                            {
                                x0 = x;
                            }else if(a == 2)
                            {
                                xn = x;
                            }else if(a == 3)
                            {
                                y0 = y;
                            }else
                            {
                                yn = y;
                            }
                        }
                        int a , b;
                        if(y0 > yn)b = 0;
                        else if(x0 > xn)a = 0;
                        else
                        {
                            a = (xn - x0);
                            b = (yn - y0);
                        }
                        printf("%d\n",a*b);
                }