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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
$n = intval(fgets(STDIN));
$A = array_map("intval", explode(" ", trim(fgets(STDIN))));

$plus = [];
$minus = [];
foreach($A as $a){
  if($a >= 0){
    $plus[] = $a;
  }else{
    $minus[] = $a;
  }
}
if($plus && $minus){//両方ある場合
  $sum = 0; 
  foreach($A as $a){
    $sum+=abs($a);
  }
  echo $sum,"\n";
  //マイナスのいずれかでプラスが残り1個になるまでプラスを吸収
  $m = array_shift($minus);
  while(count($plus) > 1){
    $p = array_shift($plus);
    echo "$m $p\n";
    $m-=$p;
  }
  $p = array_shift($plus);
  while(count($minus)>0){
    $m_ = array_shift($minus);
    echo "$p $m_\n";
    $p-=$m_;
  }
  echo $p, " ", $m;
  exit;
}
if(!$plus){//全てマイナス
  $plus = $minus;
  rsort($plus);
  for($i = 1; $i < $n - 1; $i++){
    $line[] = $plus[0]." ".$plus[$i];
    $plus[0]-=$plus[$i];
  }
  $line[] = $plus[0].' '.$plus[$n-1];
  echo ($plus[0]-$plus[$n-1])."\n";
  echo implode("\n", $line);
  exit;
}

if(!$minus){
  sort($plus);
  for($i = 1; $i < $n - 1; $i++){
    $line[] = $plus[0]." ".$plus[$i];
    $plus[0]-=$plus[$i];
  }
  $line[] = $plus[$n-1]." ".$plus[0];
  echo ($plus[$n-1]-$plus[0])."\n";
  echo implode("\n", $line);
  exit;
}