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 numpy as np
xlist = []
ylist = []
N = input()
N = int(N)
li = list(map(int,input().split()))
linp = np.array(li)
next_flag = 0
sellist = []
for i in range(0,100000):
    if(len(li) ==2):
        next_flag = 2
        break
    else:
        linp = np.array(li)
        minus_idx_size = (np.where(linp < 0))[0].size
        if(minus_idx_size==1):
            next_flag = 1
            break
        elif(minus_idx_size==0):
            sa = min(li) - max(li)
            li.remove(min(li))
            li.remove(max(li))
            sellist.append([min(li),max(li)])
            li.append(sa)
        else:
            sa = max(li) - min(li)
            li.remove(min(li))
            li.remove(max(li))
            sellist.append([max(li),min(li)])
            li.append(sa)

if(next_flag==2):
    sellist.append([max(li),min(li)])
    print(max(li)-min(li))
elif(next_flag==1):
    while(len(li)==2):
        sa = min(li) - max(li)
        li.remove(min(li))
        li.remove(max(li))
        li.append(sa)
        sellist.append([min(li),max(li)])
    sellist.append([max(li),min(li)])
    print(max(li)-min(li))
    for i in range(0,len(sellist)):
        print(sellist[i][0],sellist[i][1])