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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.util.ArrayList;
 
class Main
{
  public static void main (String[] arg)
  {
    Scanner scan = new Scanner(System.in);
    
    int A = Integer.parseInt(scan.next()); //冷蔵庫    
    int B = Integer.parseInt(scan.next()); //電子レンジ
    int M = Integer.parseInt(scan.next()); //割引
    
    int[] ref = new int[A]; //冷蔵
    int[] mic = new int[B]; //レンジ
    
    //冷蔵庫の値段入れる
    for(int i = 0; i < A;i++){
      ref[i] = Integer.parseInt(scan.next());
    }
    
    //レンジの値段入れる
    for(int i = 0; i < B;i++){
      mic[i] = Integer.parseInt(scan.next());
    }
    
    int cost;
    
    int min_ref = 100001;
    int min_mic = 100001;
    
    
    for(int i = 0; i < A;i++){
      if(ref[i] < min_ref){
        min_ref = ref[i];
      }
    }
    for(int i = 0; i < B;i++){
      if(mic[i] < min_mic){
        min_mic = mic[i];
      }
    }
    
    cost = min_ref + min_mic;
    
    for(int i = 0; i < M ;i++){
      int point_a = Integer.parseInt(scan.next());
      int point_b = Integer.parseInt(scan.next());
      int discount = Integer.parseInt(scan.next());
      
      int tmp = ref[(point_a - 1)] + mic[(point_b - 1)] - discount;
      
      if(tmp < cost){
        cost = tmp;
      }
    }
    
    System.out.println(cost);
  }
}