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: Runtime Error)

import java.util.*;

public class Main{ 
  
  public static void main(String[] args) throws Exception{
    
    Scanner sc = new Scanner(System.in);
    
    int A = sc.nextInt();
    int B = sc.nextInt();
    int M = sc.nextInt();
     
    
    if(A>=1 && A<=100000 && B>=1 && B<=100000 && M>=1 && M<=100000){
    int[] aList = new int[A];
    int[] bList = new int[B];
    
    
    for(int i = 0; i < A; ++i){
      int next = sc.nextInt();
      if(next != 0){
       aList[i] = next;
      }
    }
    int MinA = aList[0];
    for(int i = 1; i < A; ++i){
      if(MinA >= aList[i]){
        MinA = aList[i];
      }
    }
    
    for(int i = 0; i < B; ++i){
      int next = sc.nextInt();
      if(next != 0){
      bList[i] = next;
      }
    }
    int MinB = bList[0];
    for(int i = 1; i < A; ++i){
      if(MinB >= bList[i]){
        MinB = bList[i];
      }
    }
    
    int AB = MinA + MinB;
    
    int a = 0;
    int b = 0;
    int c = 0;
    int ans = 0;
    for(int i = 0; i < M; ++i){
          a = sc.nextInt();
          if(a > A){
            throw new Exception("ダメです");
          }
      
          b = sc.nextInt();
          if(b > B){
            throw new Exception("ダメです");
          }
          c = sc.nextInt();
          ans = aList[a-1] + bList[b-1] - c;
         if(AB > ans){
            AB = ans;   
        } 
   }
    
    System.out.println(AB);
    }else{
       System.out.println("ダメです");
    }
  }
}