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 {
        Scanner sc = new Scanner(System.in);
        //冷蔵庫種類
        int refnum = sc.nextInt();
        //電子レンジ種類
        int micnum = sc.nextInt();
        //割引券
        int dknum = sc.nextInt();
		//冷蔵庫の最小コスト
        int ref[] = new int[refnum];
        int refmin = 100001;
        for(int i = 0; i < refnum; i++){
        	ref[i] = sc.nextInt();
            if(ref[i] < refmin){
            	refmin = ref[i];
            }
        }
        //電子レンジ最小コスト
        int mic[] = new int[micnum];
        int micmin = 100001;
        for(int i = 0; i < micnum; i++){
        	mic[i] = sc.nextInt();
            if(mic[i] < micmin){
            	micmin = mic[i];
            }
        }
        //割引券最小コスト
        int dk[] = new int[3];
        int dkmin = 100001;
        for(int i = 0; i < dknum; i++){
        	for(int j = 0; j < 3; j++){
            	dk[j] = sc.nextInt();
            }
            if(dkmin > ref[dk[0] - 1] + mic[dk[1] - 1] - dk[2]){
            	dkmin = ref[dk[0] - 1] + mic[dk[1] -1] - dk[2];
            }
        }
        //割引券有りと無しでどちらが安いか
        if(refmin + micmin < dkmin){
        	System.out.println(refmin + micmin);
        }else if(refmin + micmin >= dkmin){
        	System.out.println(dkmin);
        }
    }
}