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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/* Code by pedroslrey *
 *     march 8        *
 *    Sunday          */

#include <bits/stdc++.h>

using namespace std;

using lli = long long int;

const int INF = 1000000007;
const lli LLINF = 9223372036854775800;

#define debug(args...) fprintf(stderr, args)
#define show(x) fprintf(stderr, "[DEBUG] -> %d\n", x)

int as[100010];
int bs[100010];

int main() {
	int a, b, m;
	scanf("%d%d%d", &a, &b, &m);
	int menor = INF;
	for (int i = 0; i < a; ++i) {
		scanf("%d", &as[i]);
		if (as[i] < menor) menor = as[i];
	}
	int omenor = INF;
	for (int i = 0; i < b; ++i) {
		scanf("%d", &bs[i]);
		if (bs[i] < omenor) omenor = bs[i];
	}
	int min = INF;
	for (int i = 0; i < m; ++i) {
		int x, y, c;
		scanf("%d%d%d", &x, &y, &c);
		int k = as[x-1] + bs[x-1] - c;
		if (k < min) min = k;
	}
	if (omenor + menor < min) min = omenor + menor;
	printf("%d\n", min);
}