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: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
//        String ans = "";

        int[] abm = Arrays.stream(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        int[] an = Arrays.stream(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        int[] bn = Arrays.stream(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();

        int mostCheapCoupon = 999999;
        for (int i = 0; i < abm[2]; i++) {
            int[] xyc = Arrays.stream(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            int usedCoupon = an[xyc[0] - 1] + bn[xyc[1] - 1] - xyc[2];
            if (usedCoupon < mostCheapCoupon) {
                mostCheapCoupon = usedCoupon;
            }
        }
        int cheapestAn = 999999;
        for(int i=0; i<an.length; i++) {
            if (an[i] < cheapestAn) cheapestAn = an[i];
        }
        int cheapestBn = 999999;
        for(int i=0; i<bn.length; i++) {
            if (bn[i] < cheapestBn) cheapestBn = bn[i];
        }
        int mostCheap = cheapestAn + cheapestBn;
        if (mostCheapCoupon < mostCheap) mostCheap = mostCheapCoupon;

        System.out.println(mostCheap);
    }
}