Problem:
Score : 500 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on a blackboard.

We will repeat the following operation N-1 times so that we have only one integer on the blackboard.

Choose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.

Find the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.

Constraints

2 \leq N \leq 10^5

-10^4 \leq A_i \leq 10^4

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.

Here x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.

If there are multiple sequences of operations that maximize the final integer, any of them will be accepted.

M
x_1 y_1
:
x_{N-1} y_{N-1}

Sample Input 1

3
1 -1 2

Sample Output 1

4
-1 1
2 -2

If we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2, 2).

Then, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).

In this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.

Sample Input 2

3
1 1 1

Sample Output 2

1
1 1
1 0

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

(defun split (input stack-string output-list)
  (let ((chara (car input)))
    (case chara
          ((nil) (append output-list (list stack-string)))
          (#\space (split (cdr input)
                                  '()
                                  (append output-list (list stack-string))))
          (otherwise (split (cdr input)
                                    (concatenate 'string stack-string (list chara))
                                    output-list)))))

(defun input-to-list (input)
  (mapcar #'parse-integer (split (concatenate 'list input)
                                 '()
                                 '())))

(defparameter n (read))
(defparameter nums (input-to-list (read-line)))

(defun format-hands (biggest smallest rest-nums)
  (if rest-nums
      (progn (format t "~d ~d~%" smallest (car rest-nums))
             (format-hands biggest
                           (- smallest (car rest-nums))
                           (cdr rest-nums)))
      (format t "~d ~d~%" biggest smallest)))

(let* ((biggest (apply #'max nums))
      (smallest (apply #'min nums))
      (rest-nums (remove biggest
                         (remove smallest
                                 nums
                                 :count 1)
                         :count 1)))
  (format t "~d~%" (- biggest (apply #'- (cons smallest rest-nums))))
  (format-hands biggest smallest rest-nums))