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: Runtime Error)

import numpy as np


N = int(input())

poss, negs = [], []
npos, nneg = 0, 0
for a in input().split():
    ia = int(a)
    if ia < 0:
        negs.append(ia)
        nneg += 1
    else:
        poss.append(ia)
        npos += 1

if N == 2:
    a1, a2 = (poss + negs)
    if a1 < a2:
        print(a2 - a1)
        print(a2, a1)
    else:
        print(a1 - a2)
        print(a1, a2)
    exit(1)

if nneg == 0:
    print(sum(poss) - min(poss) * 2)
    argmin = np.array(poss).argmin()
    minpos = poss.pop(argmin)
    pos = poss.pop()
    print(minpos, pos)
    negs.append(minpos - pos)
    npos -= 2
    nneg += 1
elif npos == 0:
    print(-sum(negs) + max(negs) * 2)
    argmax = np.array(negs).argmax()
    maxneg = negs.pop(argmax)  # -1とか
    neg = negs.pop()  # -5とか
    print(maxneg, neg)
    poss.append(maxneg - neg)
    nneg -= 2
    npos += 1
else:
    print(sum(poss) - sum(negs))

if npos > nneg:
    for _ in range(npos - nneg):
        pos, neg = poss.pop(), negs.pop()
        print(neg, pos)
        negs.append(neg - pos)
else:
    for _ in range(nneg - npos):
        pos, neg = poss.pop(), negs.pop()
        print(pos, neg)
        poss.append(pos - neg)

for _ in range(nneg - 1):
    pos, neg = poss.pop(), negs.pop()
    print(neg, pos)
    negs.append(neg - pos)
    pos, neg = poss.pop(), negs.pop()
    print(pos, neg)
    poss.append(pos - neg)

pos, neg = poss.pop(), negs.pop()
print(pos, neg)