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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
 
import java.util.*;
import java.lang.*;
import java.io.*;

@SuppressWarnings("unchecked")
public class Main implements Runnable {

  static BufferedReader in;
  static PrintWriter out;
 
  public static void main(String[] args) {
      new Thread(null, new Main(), "whatever", 1<<29).start();
  }


  /* Iterative Function to calculate 
    (x^y)%p in O(log y) */
    static long power(long x, long y, long p) 
    { 
          
        // Initialize result 
        long res = 1L; 
      
        // Update x if it is more than or 
        // equal to p 
        x = x % p; 
                      
        while (y > 0L) 
        { 
              
            // If y is odd, multiply x 
            // with result 
            if (y % 2 == 1L) 
                res = (res * x) % p; 
      
            // y must be even now 
            y = y >> 1L; // y = y/2 
            x = (x * x) % p; 
        } 
          
        return res; 
    } 

    // Returns n^(-1) mod p 
    static long modInverse(long n, long p) 
    { 
        return power(n, p-2, p); 
    } 
      
    // Returns nCr % p using Fermat's 
    // little theorem. 
    static long nCrModPFermat(long n, long r, 
                                    long p) 
    { 
          
        // Base case 
        if (r == 0L) 
            return 1L; 
      
        // Fill factorial array so that we 
        // can find all factorial of r, n 
        // and n-r 
        long fac = 1L;
          
        for (int i = 1 ;i <= r; i++) {
          fac = (fac * (n-(i-1))) % p;
          fac = (fac * modInverse(i, p)) % p;
        }
      
        return fac; 
    }
 
  public void run() {
    in = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out, false);
 
    try
    {
      // in = new BufferedReader(new FileReader("class_treasurer.txt"));
      // out = new PrintWriter("output.txt");

      int t,x1,n,aLen,bLen,mLen,i;
      String str;
      String[] token;

      str=in.readLine().trim();
      token=str.split(" ");

      aLen=Integer.parseInt(token[0]);
      bLen=Integer.parseInt(token[1]);
      mLen=Integer.parseInt(token[2]);

      int[] a=new int[aLen];
      int[] b=new int[bLen];

      str=in.readLine().trim();
      token=str.split(" ");

      int minA=Integer.MAX_VALUE;
      for(i=0;i<aLen;i++) {
        a[i]=Integer.parseInt(token[i]);
        minA=Math.min(a[i],minA);
      }

      str=in.readLine().trim();
      token=str.split(" ");

      int minB=Integer.MAX_VALUE;
      for(i=0;i<bLen;i++) {
        b[i]=Integer.parseInt(token[i]);
        minB=Math.min(b[i],minB);
      }

      int min=Integer.MAX_VALUE;

      for(i=0;i<mLen;i++) {
        str=in.readLine().trim();
        token=str.split(" ");

        int x=Integer.parseInt(token[0])-1;
        int y=Integer.parseInt(token[1])-1;
        int c=Integer.parseInt(token[2]);

        min=Math.min(min, a[x]+b[y]-c);
      }

      min=Math.min(min, minA+minB);

      out.println(min);

      out.flush();
      out.close();
    }
    catch(Exception e) {
      e.printStackTrace();
    }
  }
}