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: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

;; BEGIN_INSERTED_CONTENTS
(defun bisect-left (target value &key (start 0) end (predicate #'<) (key #'identity))
  "TARGET := vector | function
PREDICATE := strict order

Returns the smallest index (or input) i that fulfills TARGET[i] >= VALUE, where
'>=' is the complement of PREDICATE. TARGET must be monotonically non-decreasing with
respect to PREDICATE. This function returns END if VALUE exceeds TARGET[END-1]. Note
that the range [START, END) is half-open. END must be explicitly specified if
TARGET is function. KEY is applied to each element of TARGET before comparison."
  (declare (function key predicate)
           ((integer 0 #.most-positive-fixnum) start)
           ((or null (integer 0 #.most-positive-fixnum)) end))
  (macrolet
      ((body (accessor &optional declaration)
         `(cond ((assert (<= start end)))
                ((= start end) end)
                ((funcall predicate (funcall key (,accessor target (- end 1))) value)
                 end)
                (t (labels ((%bisect-left (l r)
                              ,@(list declaration)
                              (let ((mid (ash (+ l r) -1)))
                                (if (= mid l)
                                    (if (funcall predicate (funcall key (,accessor target l)) value)
                                        r
                                        l)
                                    (if (funcall predicate (funcall key (,accessor target mid)) value)
                                        (%bisect-left mid r)
                                        (%bisect-left l mid))))))
                     (%bisect-left start (- end 1)))))))
    (etypecase target
      (vector
       (let ((end (or end (length target))))
         (body aref (declare ((integer 0 #.most-positive-fixnum) l r)))))
      (function
       (assert end)
       (body funcall)))))

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

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;; Body

(defun main ()
  (declare #.OPT (inline sort))
  (let* ((n (read))
         (as (make-array n :element-type 'fixnum)))
    (dotimes (i n) (setf (aref as i) (read-fixnum)))
    (setf as (sort as #'<))
    (let ((a-min (aref as 0))
          (a-max (aref as (- n 1)))
          (pivot (bisect-left as 0))
          (out (make-string-output-stream :element-type 'base-char)))
      (declare (fixnum a-min a-max))
      (loop for i from (max pivot 1) below (- n 1)
            do (format out "~D ~D~%" a-min (aref as i))
               (setf a-min (- a-min (aref as i))))
      (loop for i from 1 below (min pivot (- n 1))
            do (format out "~D ~D~%" a-max (aref as i))
               (setf a-max (- a-max (aref as i))))
      (format out "~D ~D~%" a-max a-min)
      (println (- a-max a-min))
      (write-string (get-output-stream-string out)))))

#-swank(main)


;; For Test
#+swank
(defun io-equal (in-string out-string &optional (func #'main))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNC, and checks the string
output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (and (> (length s) 0)
                      (eql (char s (- (length s) 1)) #\Linefeed))
                 s
                 (uiop:strcat s uiop:+lf+))))
    (equal (ensure-last-lf out-string)
           (with-output-to-string (out)
             (let ((*standard-output* out))
               (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                 (funcall func)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    (run-program "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  (let ((*standard-output* out))
    (etypecase thing
      (null ; Runs #'MAIN with the string on clipboard
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname ; Runs #'MAIN with the string in a text file
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3
1 -1 2
"
    "4
-1 1
2 -2
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3
1 1 1
"
    "1
1 1
1 0
")))