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 Python (3.4.3) (judge verdict: Accepted)

n=int(input())
a=list(map(int,input().split()))
a.sort()
A=[a[0]]
x=0
sum=sum(a)
sumL=-9999999999
if n==2:
  print(max(a)-min(a))
  print(max(a),min(a))
else:
  for i in range(1,n):
    A.append(A[i-1]+a[i])
  for i in range(1,n):
    if sumL<-A[i-1]+sum-A[i-1]:
      sumL=-A[i-1]+sum-A[i-1]
      x=i
  print(sumL)
  L1=a[0:x]
  L2=a[x:n]

  if x!=1:
    print(L2[0],L1[0])
    z=L2[0]-L1[0]
    for i in range(1,x-1):
      print(z,L1[i])
      z=z-L1[i]
  else:
    z=L2[0]

  if x!=n-1:
    print(L1[x-1],L2[1])
    y=L1[x-1]-L2[1]
    for i in range(2,len(L2)):
      print(y,L2[i])
      y=y-L2[i]
  else:
    y=L1[len(L1)-1]

  print(z,y)