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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <ctype.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>

#define N_MAX (100)
#define P_MAX (100)
#define DP_ARRAY_SIZE (N_MAX * P_MAX / 32 + 1)

#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define ABS(a) ((a) < 0 ? -(a) : (a))
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))

int compare_f(const void *a, const void *b) {
	return *((int64_t *)a) < *((int64_t *)b) ? -1 : 1;
}

int compare_f2(const void *a, const void *b) {
	return *((uint64_t *)a) > *((uint64_t *)b) ? -1 : 1;
}

static size_t comb(const size_t n, const size_t r) {
	size_t result = 1;

	for (size_t i = 0; i < r; i++) {
		result *= n - i;
		result /= i + 1;
	}

	return result;
}

static uint64_t combU64(const uint64_t n, const uint64_t r) {
	uint64_t result = 1;

	for (uint64_t i = 0; i < r; i++) {
		result *= n - i;
		result /= i + 1;
	}

	return result;
}

static uint64_t gcd(uint64_t m, uint64_t n)
{
	uint64_t temp;

	while (m%n != 0) {
		temp = n;
		n = m % n;
		m = temp;
	}

	return n;
}

int main(void) {
	size_t W, H, N;

	scanf("%zu %zu %zu\n", &W, &H, &N);

	bool isWhite[100][100];
	for (size_t i = 0; i < W - 1; i++) {
		for (size_t j = 0; j < H - 1; j++) {
			isWhite[i][j] = true;
		}
	}

	for (size_t i = 0; i < N; i++) {
		size_t x, y, a;
		scanf("%zu %zu %zu", &x, &y, &a);
		if (i < N - 1) {
			scanf("\n");
		}

		if (a == 1) {
			for (size_t i = 0; i < x; i++) {
				for (size_t j = 0; j < H - 1; j++) {
					isWhite[i][j] = false;
				}
			}
		}
		else if (a == 2) {
			for (size_t i = x; i < W - 1; i++) {
				for (size_t j = 0; j < H; j++) {
					isWhite[i][j] = false;
				}
			}
		}
		else if (a == 3) {
			for (size_t i = 0; i < W - 1; i++) {
				for (size_t j = 0; j < y; j++) {
					isWhite[i][j] = false;
				}
			}
		}
		else {
			for (size_t i = 0; i < W - 1; i++) {
				for (size_t j = y; j < H - 1; j++) {
					isWhite[i][j] = false;
				}
			}
		}
	}

	size_t count = 0;

	for (size_t i = 0; i < W - 1; i++) {
		for (size_t j = 0; j < H - 1; j++) {
			if (isWhite[i][j]) {
				count++;
			}
		}
	}

	printf("%zu\n", count);

	return 0;
}