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: Wrong Answer)

fn main() {
    let type_counts = read();
    let mut type_counts = type_counts.split(' ').map(|s| s.parse::<usize>().unwrap());
    let _reizouko_cnt = type_counts.next().unwrap();
    let _denshirenji_cnt = type_counts.next().unwrap();
    let waribikiken_cnt = type_counts.next().unwrap();

    let reizoukos = read();
    let reizoukos: Vec<usize> = reizoukos.split(' ').map(|s| s.parse::<usize>().unwrap()).collect();
    let denshirenjis = read();
    let denshirenjis: Vec<usize> = denshirenjis.split(' ').map(|s| s.parse::<usize>().unwrap()).collect();
    let mut current_min = reizoukos[0] + denshirenjis[0];
    for _ in 0..waribikiken_cnt {
        let values = read();
        let mut values = values.split(' ').map(|s| s.parse::<usize>().unwrap());
        let target_reizouko = values.next().unwrap();
        let target_denshirenji = values.next().unwrap();
        let waribiki_nedan = values.next().unwrap();

        let applied = reizoukos[target_reizouko - 1] + denshirenjis[target_denshirenji - 1] - waribiki_nedan;
        if current_min > applied {
            current_min = applied;
        }
    }
    println!("{}", current_min);
}
fn read() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}