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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def solve():
    N = int(input())
    A = list(map(int,input().split()))
    neg = []
    pos = []
    for a in A:
        if a < 0:
            neg.append(a)
        else:
            pos.append(a)
    
    neg.sort()
    pos.sort()
    
    op = []
    if len(neg) == N:
        for i in range(len(neg)-1):
            op.append("{0} {1}".format(neg[-1], neg[i]))
            neg[-1] -= neg[i]
        
        printAns(neg[-1], op)
        return
    
    if len(pos) == N:
        for i in range(len(pos)-2):
            op.append("{0} {1}".format(pos[i+1], pos[i]))
            pos[i+1] = pos[i] - pos[i+1]
        
        op.append("{0} {1}".format(pos[-1], pos[-2]))
        
        printAns(pos[-1] - pos[-2],op)
        return
    
    for i in range(len(pos)-1):
        op.append("{0} {1}".format(neg[0], pos[i]))
        neg[0] -= pos[i]
    
    for ne in neg:
        op.append("{0} {1}".format(pos[-1], ne))
        pos[-1] -= ne
    
    printAns(pos[-1], op)

def printAns(M, op):
    print(M)
    print(*op, sep='\n')
    
if __name__ == '__main__':
    solve()