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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

func main() {
	var A, B, M int
	var ap [100000]int
	var bp [100000]int
	var x, y, c, p int

	fmt.Scan(&A, &B, &M)

	scanner := bufio.NewScanner(os.Stdin)

	amin := 10000000
	scanner.Scan()
	tmp1 := strings.Split(scanner.Text(), " ")
	for k, i := range tmp1 {
		j, err := strconv.Atoi(i)
		if err != nil {
			panic(err)
		}
		if amin > j {
			amin = j
		}
		ap[k] = j
	}

	bmin := 100000000
	scanner.Scan()
	tmp1 = strings.Split(scanner.Text(), " ")
	for k, i := range tmp1 {
		j, err := strconv.Atoi(i)
		if err != nil {
			panic(err)
		}
		if bmin > j {
			bmin = j
		}
		bp[k] = j
	}

	min := amin + bmin
	// fmt.Println(min)

	for i := 0; i < M; i++ {
		scanner.Scan()
		fmt.Sscan(scanner.Text(), &x, &y, &c)
		p = ap[x-1] + bp[y-1] - c
		// fmt.Printf("%v %v %v %v\n", x, y, c, p)
		if min > p {
			min = p
		}
	}
	// fmt.Printf("A %v \n", ap[0:5])
	// fmt.Printf("B %v %v\n", bp[0:5], bp[1])

	// tmp := 0
	// for i := 0; i < A; i++ {
	// 	// fmt.Println("a")
	// 	for j := 0; j < B; j++ {
	// 		// fmt.Println("b")
	// 		tmp = ap[i] + bp[j]
	// 		valuable_discount := 0
	// 		for k := 0; k < M; k++ {
	// 			// fmt.Printf("m, k:%d, x[k]:%d, y[k]:%d, c[k]:%d\n", k, x[k], y[k], c[k])
	// 			if x[k] == i+1 || y[k] == j+1 {
	// 				// TODO: find most big discount?
	// 				if valuable_discount < c[k] {
	// 					valuable_discount = c[k]
	// 				}
	// 				// fmt.Printf("asdf %d\n", valuable_discount)
	// 			}
	// 		}
	// 		tmp -= valuable_discount
	// 		if min > tmp {
	// 			min = tmp
	// 		}
	// 	}
	// }
	fmt.Println(min)
}