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: Wrong Answer)

import bisect
N = int(input())
A = list(map(int,input().split()))
if N == 2:
  print(max(A)-min(A))
  print(*A)
  exit()
A.sort()
#print(A)
plus = []
minus = []
for i in range(N):
  if A[i] < 0:
    minus.append(A[i])
  else:
    plus.append(A[i])
minus.sort(reverse = True)
plus.sort()
if len(plus) == 0:
  plus.append(minus.pop())
elif len(minus) == 0:
  minus.append(plus.pop())
#print(plus)
#print(minus)
tmp = plus[-1]
tmp2 = minus[-1]
ans = []
cnt = 0
for i in range(len(plus)-1):
  ans.append([tmp2,plus[i]])
  tmp2 -= plus[i]
minus[-1] = tmp2
for i in range(len(minus)):
  ans.append([tmp,minus[i]])
  tmp -= minus[i]
print(tmp)
for i in range(N-1):
  print(*ans[i])