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: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include <time.h>
typedef long long ll;
typedef long double ld;
#define INF (1LL<<60)
#define MOD1 1000000007
/*swap 交換*/
void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a=c;}
/*2つのうち大きい数を返す*/
ll max2(ll a,ll b){return a>=b?a:b;}
/*2つのうち小さい数を返す*/
ll min2(ll a,ll b){return a>=b?b:a;}
/*絶対値*/
ll ABS(ll a){return a>=0?a:(-a);}
typedef struct{
    ll aa;
    ll bb;
}frequent;
// 小大
int compare(const void *a, const void *b){return *(ll *)a - *(ll *)b;}

int main(void){
    ll w,h,n,i,ans=0;
    scanf("%lld%lld%lld",&w,&h,&n);
    ll x[n],y[n],a[n],l,r,u,d;
    for(i=0;i<n;i++){
        scanf("%lld%lld%lld",&x[i],&y[i],&a[i]);
    }
    // for(i=0;i<w;i++){
    //     for(j=0;j<h;j++){
    //         color[w][h]=0;
    //     }
    // }
    l=0;
    r=w;
    d=0;
    u=h;
    for(i=0;i<n;i++){
        if(a[i]==1){
            // for(j=0;j<x[i];j++){
            //     for(k=0;k<h;k++){
            //         color[j][k]=1;
            //     }
            // }
            l=max2(l,x[i]);
        }
        if(a[i]==2){
            // for(j=x[i]+1;j<w;j++){
            //     for(k=0;k<h;k++){
            //         color[j][k]=1;
            //     }
            // }
            r=min2(r,x[i]);
        }
        if(a[i]==3){
            // for(j=0;j<w;j++){
            //     for(k=0;k<y[i];k++){
            //         color[j][k]=1;
            //     }
            // }
            d=max2(d,y[i]);
        }
        if(a[i]==4){
            // for(j=0;j<w;j++){
            //     for(k=y[i]+1;k<h;k++){
            //         color[j][k]=1;
            //     }
            // }
            u=min2(u,y[i]);
        }
    }
    // for(i=0;i<w;i++){
    //     for(j=0;j<h;j++){
    //         if(color[i][j]==0) ans++;
    //     }
    // }
    if(l<r && d<u) ans=(r-l)*(u-d);
    printf("%lld\n",ans);
    return 0;
}