Problem:
Score : 200 points

Problem Statement

You are visiting a large electronics store to buy a refrigerator and a microwave.

The store sells A kinds of refrigerators and B kinds of microwaves. The i-th refrigerator ( 1 \le i \le A ) is sold at a_i yen (the currency of Japan), and the j-th microwave ( 1 \le j \le B ) is sold at b_j yen.

You have M discount tickets. With the i-th ticket ( 1 \le i \le M ), you can get a discount of c_i yen from the total price when buying the x_i-th refrigerator and the y_i-th microwave together. Only one ticket can be used at a time.

You are planning to buy one refrigerator and one microwave. Find the minimum amount of money required.

Constraints

All values in input are integers.

1 \le A \le 10^5

1 \le B \le 10^5

1 \le M \le 10^5

1 \le a_i , b_i , c_i \le 10^5

1 \le x_i \le A

1 \le y_i \le B

c_i \le a_{x_i} + b_{y_i}

Input

Input is given from Standard Input in the following format:

A B M
a_1 a_2 ... a_A
b_1 b_2 ... b_B
x_1 y_1 c_1
\vdots
x_M y_M c_M

Output

Print the answer.

Sample Input 1

2 3 1
3 3
3 3 3
1 2 1

Sample Output 1

5

With the ticket, you can get the 1-st refrigerator and the 2-nd microwave for 3+3-1=5 yen.

Sample Input 2

1 1 2
10
10
1 1 5
1 1 10

Sample Output 2

10

Note that you cannot use more than one ticket at a time.

Sample Input 3

2 2 1
3 5
3 5
2 2 2

Sample Output 3

6

You can get the 1-st refrigerator and the 1-st microwave for 6 yen, which is the minimum amount to pay in this case.
Note that using a ticket is optional.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

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

int compare(const void *a,const void *b){
    if(*(int *)a>*(int *)b)return 1;
    return -1;
}
int main()
{   int A,B,M;
    scanf("%d%d%d",&A,&B,&M);
    int a[A],b[B];
    for(int i=0;i<A;i++){
        scanf("%d",&a[i]);
    }
    for(int i=0;i<B;i++){
        scanf("%d",&b[i]);
    }
    int x[M],y[M],c[M];
    int vl[M+1];
    for(int i=0;i<M;i++){
        scanf("%d%d%d",&x[i],&y[i],&c[i]);
        vl[i]=a[x[i]-1]+b[y[i]-1]-c[i];
    }
    qsort(a,A,sizeof(int),compare);
    qsort(b,B,sizeof(int),compare);
    vl[M]=a[0]+b[0];
    qsort(vl,M+1,sizeof(int),compare);
    printf("%d",vl[0]);

    return 0;
}