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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  (declare (inline read-byte)
           #-swank (sb-kernel:ansi-stream in))
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (read-byte in nil 0))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setq minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
	 (let* ((byte (%read-byte)))
	   (if (<= 48 byte 57)
	       (setq result (+ (- byte 48) (the (integer 0 #.(floor most-positive-fixnum 10)) (* result 10))))
	       (return (if minus (- result) result))))))))

(defun main ()
  (let* ((a-num (read))
	 (b-num (read))
	 (m-num (read))
	 (a-price (make-array a-num))
	 (b-price (make-array b-num))
	 (price 100000))
    (dotimes (n a-num)
      (setf (aref a-price n) (read)))
    (dotimes (n b-num)
      (setf (aref b-price n) (read)))
    (dotimes (i m-num)
      (let* ((a-disc-idx (read))
	     (b-disc-idx (read))
	     (disc-price (read))
	     (result (- (+ (aref a-price (1- a-disc-idx)) (aref b-price (1- b-disc-idx))) disc-price)))
	(if (< result price) 
	    (setq price result))))
    (setq a-price (sort a-price #'<))
    (setq b-price (sort b-price #'<))
    (if (< (+ (aref a-price 0) (aref b-price 0)) price)
	(setq price (+ (aref a-price 0) (aref b-price 0))))
    (format t "~a~%" price)))

(main)