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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;
using static System.Math;
using static Math2;
using static io;


class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 29;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;



    public void Solve()
    {
        var o = intm;
        var A = o[0];
        var B = o[1];
        var m = o[2];
        var a = intm;
        var b = intm;
        var ans = a.Min() + b.Min();
        for (int i = 0; i < m; ++i)
        {
            var oo = intm;
            oo[0]--;
            oo[1]--;
            chmin(ref ans, a[oo[0]] + b[oo[1]] - oo[2]);
        }
        write(ans);
    }

}



public static class Math2
{
    public static long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }
    public static int pow(int i, int n, int MOD = 1000000007)
    {
        int res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public static long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public static BigInteger bgcd(BigInteger i, BigInteger y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static BigInteger blcm(BigInteger i, BigInteger y)
    {
        return i * y / bgcd(i, y);
    }

    public static Dictionary<long, int> primefactorization(long N)
    {

        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public static List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public static void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }
    public static void chmin<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) > 0) a = b;
    }
    public static void chmax<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) < 0) a = b;
    }

}

public static class io
{
    //in
    public static string str => Console.ReadLine();

    public static string[] strm => str.Split(' ');

    public static long[] longm => strm.Select(long.Parse).ToArray();
    public static int[] intm => strm.Select(int.Parse).ToArray();
    public static char[] charm => str.ToArray();
    public static double[] doublem => strm.Select(double.Parse).ToArray();
    public static long long1 => longm[0];
    public static int int1 => intm[0];
    public static char char1 => charm[0];
    public static double double1 => doublem[0];
    public static void write(string a) => Console.WriteLine(a);
    public static void write(params object[] i) => write(string.Join(" ", i));
    public static void write<T>(IEnumerable<T> a) => write(string.Join(" ", a));
    public static void yn(bool i) { if (i) write("Yes"); else write("No"); }

}