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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;



public class CompetitiveProgramming
{

  public void Solve()
  {
    var N = Int1;
    var A = Ints;
    Array.Sort(A);
    if (A[0] > 0)
    {
      Write(A.Skip(1).Sum() - A[0]);
      for (int i = 0; i < N - 2; ++i)
      {
        Write(A[0], A[i + 1]);
        A[0] -= A[i + 1];
      }
      Write(A[N - 1], A[0]);
      return;
    }
    else if (A[N - 1] < 0)
    {
      long an = 0;
      A = A.Reverse().ToArray();
      for (int i = 0; i < N - 1; ++i) an -= A[i + 1];
      Write(A[0] + an);
      for (int i = 0; i < N - 1; ++i)
      {
        Write(A[0], A[i + 1]);
        A[0] -= A[i + 1];
      }
      return;
    }
    long ans = 0;
    var positive = new List<int>();
    var negative = new List<int>();
    for (int i = 0; i < N; ++i)
    {
      if (A[i] >= 0) positive.Add(A[i]);
      else negative.Add(A[i]);
      ans += Abs(A[i]);
    }
    Write(ans);
    while (positive.Count > 1)
    {
      Write(negative[0], positive.Last());
      negative[0] -= positive.Last();
      positive.RemoveAt(positive.Count - 1);
    }
    while (negative.Count > 0)
    {
      Write(positive[0], negative.Last());
      positive[0] -= negative.Last();
      negative.RemoveAt(negative.Count - 1);
    }

  }


}



public static class Graph
{
  public static long[] dijkstra(List<Tuple<long, int>>[] edge, int from, long INF = Math2.INFL)
  {
    long[] ret = Enumerable.Range(0, edge.Length).Select(_ => INF).ToArray();
    var pq = new PriorityQueue<Tuple<long, int>>((a, b) => (int)(a.Item1 - b.Item1));
    ret[from] = 0;
    pq.Enqueue(new Tuple<long, int>(0, from));
    while (pq.Count > 0)
    {
      var p = pq.Dequeue();
      var v = p.Item2;
      if (ret[v] < p.Item1) continue;
      foreach (var e in edge[v])
      {
        if (ret[e.Item2] > ret[v] + e.Item1)
        {
          ret[e.Item2] = ret[v] + e.Item1;
          pq.Enqueue(new Tuple<long, int>(ret[e.Item2], e.Item2));
        }

      }
    }
    return ret;
  }
}


public class PriorityQueue<T>
{
  List<T> _item;
  public int Count { get { return _item.Count; } }
  bool _isascend { get; set; }
  public T Peek { get { return _item[0]; } }
  Comparison<T> Comp;
  public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
  public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null)
  {
    _item = new List<T>();
    _isascend = IsAscend;
    this.Comp = cmp;
    if (list != null)
    {
      _item.AddRange(list);
      Build();
    }
  }

  private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
  private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
  private int Parent(int i)
      => (i - 1) >> 1;
  private int Left(int i)
      => (i << 1) + 1;
  public T Enqueue(T val)
  {
    int i = _item.Count;
    _item.Add(val);
    while (i > 0)
    {
      int p = Parent(i);
      if (Compare(i, p) > 0)
        Swap(i, p);
      i = p;
    }
    return val;
  }
  private void Heapify(int index)
  {
    for (int i = index, j; (j = Left(i)) < _item.Count; i = j)
    {
      if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
      if (Compare(i, j) < 0)
        Swap(i, j);
    }
  }
  public T Dequeue()
  {
    T val = _item[0];
    _item[0] = _item[_item.Count - 1];
    _item.RemoveAt(_item.Count - 1);
    Heapify(0);
    return val;
  }
  private void Build()
  {
    for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
      Heapify(i);
  }
}



public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b)
  {
    while (b > 0)
    {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = n; i >= n - r + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long n, long r)
  {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
}
public static class Utils
{

  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N)
  {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  //public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}