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 Ruby (2.7.1) (judge verdict: Wrong Answer)

A, B, M = gets.split.map &:to_i
a = gets.split.map { |i| i.to_i }
b = gets.split.map { |i| i.to_i }
discount = {}
M.times do
  temp = gets.split.map { |i| i.to_i - 1 }
  key = temp[0].to_s + "-" + temp[1].to_s
  if discount.has_key?(key)
    discount[key] = temp[2] + 1 if temp[2] > discount[key]
  else
    discount[key] = temp[2] + 1
  end
end

ans = a[0] + b[0]
A.times do |i|
  B.times do |j|
    key = i.to_s + "-" + j.to_s
    if discount.has_key?(key)
      temp = a[i] + b[j] - discount[key]
    else
      temp = a[i] + b[j]
    end
    ans = temp if temp < ans
  end
end
puts ans