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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::fmt::Debug;
use std::io;
use std::str::FromStr;

fn read_and_divide_line<T>() -> Vec<T>
where
    T: FromStr,
    <T as FromStr>::Err: Debug,
{
    let mut target_line = String::new();
    io::stdin().read_line(&mut target_line).unwrap();
    target_line
        .trim()
        .split_whitespace()
        .map(|c| T::from_str(c).unwrap())
        .collect()
}

fn main() {
    let kind_num: Vec<i64> = read_and_divide_line();
    let coupon_kind_num = kind_num[2];

    let refrigerator_prices: Vec<i64> = read_and_divide_line();
    let microwave_prices: Vec<i64> = read_and_divide_line();

    let mut each_price_combination: Vec<Vec<i64>> = vec![];

    for _ in 0..coupon_kind_num {
        each_price_combination.push(read_and_divide_line());
    }

    let mut min_price = refrigerator_prices[0] * microwave_prices[0];

    for refri_price in &refrigerator_prices {
        for microwave_price in &microwave_prices {
            let now_price = refri_price + microwave_price;
            if now_price < min_price {
                min_price = now_price;
            }
        }
    }

    for combination in each_price_combination {
        let now_price = refrigerator_prices[(combination[0] as usize) - 1]
            + microwave_prices[(combination[1] as usize) - 1]
            - combination[2];
        if now_price < min_price {
            min_price = now_price;
        }
    }

    println!("{}", min_price);
}