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.

2 3 1
3 3
3 3 3
1 2 1

5

With the ticket, you can get the $1$-st refrigerator and the $2$-nd microwave for $3+3-1=5$ yen.

1 1 2
10
10
1 1 5
1 1 10

10

Note that you cannot use more than one ticket at a time.

2 2 1
3 5
3 5
2 2 2

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.