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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdbool.h>
#include <string.h>



/*以下便利なマクロを定義する。*/

#define rep(i, min, max) for(i=min; i<=max; i=i+1)



#define if_forall(i, min, max, prop)\
	bool if_forall_condition=1;\
\
	for(i=min; i<=max; i=i+1)\
	{\
		if(!(prop))\
		{\
			if_forall_condition=0;\
			break;\
		}\
	}\
\
	if(if_forall_condition==1)\



#define if_exists(i, min, max, prop)\
	bool if_exists_condition=0;\
\
	for(i=min; i<=max; i=i+1)\
	{\
		if(prop)\
		{\
			if_exists_condition=1;\
			break;\
		}\
	}\
\
	if(if_exists_condition==1)\











/*以下便利な関数を定義する。*/

void ini_int(int array[], int num)
{
	int i=0;

	for(i=0; i<=num; i=i+1)
	{
		array[i]=0;
	}

}



void ini_char(char array[], int num)
{
	int i=0;

	for(i=0; i<=num; i=i+1)
	{
		array[i]='\0';
	}

}



int powi(int base, unsigned int exponent)
{
	int answer=1;

	answer=(int)pow((double)base, (double)exponent);

	return answer;
}



void  swap_int(int* x, int* y)
{
    int  tmp;

    tmp = *x;
    *x = *y;
    *y = tmp;
}



void  swap_int_array(int x[], int y[], int min, int max)
{
	int i;

    rep(i, min, max)
	{
		swap_int(&x[i], &y[i]);
	}
}



void  swap_char(char* x, char* y)
{
    char  tmp;

    tmp = *x;
    *x = *y;
    *y = tmp;
}



void  swap_char_array(char x[], char y[], int min, int max)
{
	int i;

    rep(i, min, max)
	{
		swap_char(&x[i], &y[i]);
	}
}



void reverse_char(char array[], int min, int max)
{
	int i;

	rep(i, min, (min+max)/2)
	{
		swap_char(&array[i], &array[min+max-i]);
	}
}



void sort_asc_int(int array[], int min, int max)
{
	int i, j;

	rep(i, min, max)
	{
		rep(j, i+1, max)
		{
			if(array[i]>array[j])
			{
				swap_int(&array[i], &array[j]);
			}
		}
	}
}



void sort_des_int(int array[], int min, int max)
{
	int i, j;

	rep(i, min, max)
	{
		rep(j, i+1, max)
		{
			if(array[i]<array[j])
			{
				swap_int(&array[i], &array[j]);
			}
		}
	}
}



void sort_asc_char_dic(int size, char array[][size], int min, int max)
{
	int i, j;

	rep(i, min, max)
	{
		rep(j, i+1, max)
		{
			if(strcmp(array[i], array[j])>0)
			{
				swap_char_array(array[i], array[j], 0, size-1);
			}
		}
	}
}



void sort_des_char_dic(int size, char array[][size], int min, int max)
{
	int i, j;

	rep(i, min, max)
	{
		rep(j, i+1, max)
		{
			if(strcmp(array[i], array[j])<0)
			{
				swap_char_array(array[i], array[j], 0, size-1);
			}
		}
	}
}



int max_int(int var1, int var2)
{
	int answer=var1;

	if(answer<var2)
	{
		answer=var2;
	}

	return answer;
}



int max_int_array(int array[], int min, int max)
{
	int i;
	int answer;

	answer=array[min];

	for(i=min+1; i<=max; i=i+1)
	{
		answer=max_int(answer, array[i]);
	}

	return answer;
}



int min_int(int var1, int var2)
{
	int answer=var1;

	if(answer>var2)
	{
		answer=var2;
	}

	return answer;
}



int min_int_array(int array[], int min, int max)
{
	int i;
	int answer;

	answer=array[min];

	for(i=min+1; i<=max; i=i+1)
	{
		answer=min_int(answer, array[i]);
	}

	return answer;
}



int max_char_dic(int size, char array[][size], int min, int max)
{
	int i;
	int answer=min;

	rep(i, min+1, max)
	{
		if(strcmp(array[answer], array[i])<0)
		{
			answer=i;
		}
	}

	return answer;
}



int min_char_dic(int size, char array[][size], int min, int max)
{
	int i;
	int answer=min;

	rep(i, min+1, max)
	{
		if(strcmp(array[answer], array[i])>0)
		{
			answer=i;
		}
	}

	return answer;
}



int sum_array(int array[], int min, int max)
{
	int i=min;
	int answer=0;

	rep(i, min, max)
	{
		answer=answer+array[i];
	}

	return answer;
}



bool containelement_int(int array[], int min, int max, int element)
{
	int i;
	bool answer=0;

	if_exists(i, min, max, array[i]==element)
	{
		answer=1;
	}

	return answer;
}



int count_differentelement_int(int array[], int min, int max)
{
	int i=min;
	int pickup[max];
	ini_int(pickup, max);
	int answer=0;

	rep(i, min, max)
	{
		if(containelement_int(pickup, 0, answer-1, array[i])==0)
		{
			pickup[answer]=array[i];
			answer=answer+1;
		}
	}

	return answer;
}



int count_equalelement_int(int array[], int min, int max, int element)
{
	int i;
	int answer=0;

	rep(i, min, max)
	{
		if(array[i]==element)
		{
			answer=answer+1;
		}
	}

	return answer;
}



int count_equalelement_char(char array[], int min, int max, char element)
{
	int i;
	int answer=0;

	rep(i, min, max)
	{
		if(array[i]==element)
		{
			answer=answer+1;
		}
	}

	return answer;
}












int main()
{
	int i;

	int W, H, N;
	scanf("%d %d %d", &W, &H, &N);

	int x[N+1], y[N+1], a[N+1];
	rep(i, 1, N)
	{
		scanf("%d %d %d", &x[i], &y[i], &a[i]);
	}

	int x_min=0, x_max=W, y_min=0, y_max=H;

	rep(i, 1, N)
	{
		if(a[i]==1)
		{
			x_min=x[i];
		}
		else if(a[i]==2)
		{
			x_max=x[i];
		}
		else if(a[i]==3)
		{
			y_min=y[i];
		}
		else if(a[i]==4)
		{
			y_max=y[i];
		}
	}
	printf("%d\n", max_int(0, (x_max-x_min)*(y_max-y_min)));
	return 0;
}