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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int A =sc.nextInt();
        int B =sc.nextInt();
        int M =sc.nextInt();
        
        int result=0;
       
       
        
        int costA[] = new int[A];
        int costB[] = new int[B];
        int coupon[] = new int[M];
        int numberA[] =new int[M];
        int numberB[] =new int[M];
        int numberM[] =new int[M];
        
        
        int Nocoupon =0;
        int CouponResult =0;
        int answer =0;
        
        int MinA =1000000;
        int MinB =1000000;
        
        for(int i=0;i<A;i++){
            costA[i]=sc.nextInt();
        }
        
        for(int j=0;j<B;j++){
            costB[j]=sc.nextInt();
        }
        
        for(int k=0;k<M;k++){
            numberA[k]=sc.nextInt();
            numberB[k]=sc.nextInt();
            numberM[k]=sc.nextInt();

        }
        
        
        Arrays.sort(costA);
        Arrays.sort(costB);
        
        Nocoupon=costA[0]+costB[0];
        answer=Nocoupon;
        
        for(int i=0;i<M;i++){
            CouponResult=(costA[numberA[i]-1]+costB[numberB[i]-1]-numberM[i]);
            if(CouponResult<Nocoupon){
                answer=CouponResult;
            }
        }
        
        
        
        System.out.println(answer);
        
    }
}