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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

abm = input('')
a = int(abm.split(' ')[0])
b = int(abm.split(' ')[1])
m = int(abm.split(' ')[2])
wdic = {}
pdic = {}
clist = input('').split(' ')
dlist = input('').split(' ')

max_w = 0
for i in range(0,m):
  win = input('').split(' ')
  wc = win[0]
  wd = win[1]
  wkey = wc + "-" + wd
  wp = int(win[2])
  if wkey in wdic.keys():
    if wp > wdic[wkey]:
      wdic[wkey] = wp
  else:
    wdic[wkey] = wp
  if wp > max_w:
    max_w = wp

for i in range(0,a):
  for j in range(0,b):
    key = str(i+1) + "-" + str(j+1)
    val = int(clist[i]) + int(dlist[j])
    w = 0
    if key in wdic.keys():
	    w = wdic[key]
    pdic[key] = val - w
    
min_price = -1

pdic2 = sorted(pdic.items(), key=lambda x:x[1],reverse=True)

for kp in pdic2:
  key = kp[0]
  price = kp[1]
  if min_price == -1:
    min_price = price
  elif price < min_price:
    min_price = price     
  if price > (min_price + max_w):
    break

print(min_price)