Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defun make-pq (alist)
  (sort (copy-alist alist) (lambda (a b) (< (car a) (car b)))))

(define-modify-macro insert-pq (pair)
                     (lambda (pq pair) (sort (cons pair pq) (lambda (a b) (< (car a) (car b))))))

(define-modify-macro remove-pq-aux () cdr)

(defmacro remove-pq (pq)
  `(let ((aux (copy-alist ,pq)))
     (REMOVE-PQ-AUX ,pq)
     (car aux)))

(let* ((n (read))
       (alen (* 3 n))
       (seq (make-array alen))
       (res 0))
  (dotimes (i alen) (setf (aref seq i) (read)))
  (setf res
    (loop for k from 0 to n
          with bpq = nil
          with spq = nil do
          (setf bpq (make-pq nil)
                spq (make-pq nil))
          (dotimes (i n)
            (let ((a (aref seq i)))
              (insert-pq bpq `(,a . ,a))))
          (dotimes (i n)
            (let ((a (aref seq (- (1- alen) i))))
              (insert-pq spq `(,(- a) . ,a))))
          (dotimes (i k)
            (let ((a (aref seq (1- (+ n k)))))
              (insert-pq bpq `(,a . ,a))
              (remove-pq bpq)))
          (dotimes (i (- n k))
            (let ((a (aref seq (- (- alen n 1) i))))
              (insert-pq spq `(,(- a) . ,a))
              (remove-pq spq)))
          maximize (- (loop for (x . y) in bpq sum y)
                      (loop for (x . y) in spq sum y))))
  (format t "~A~%" res))