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)

N = int(input())
A = list(map(int, input().split(" ")))
A.sort()

n_pos = len([a for a in A if a > 0])
operations = []
if n_pos <= (N + 1) // 2:
    pos = [a for a in A if a > 0]
    neg = [a for a in A if a <= 0]
    tmp = pos[0]
    for i in range(n_pos-1):
        operations.append((neg[i], tmp))
        tmp = neg[i] - tmp
        operations.append((pos[i+1], tmp))
        tmp = pos[i+1] - tmp
        
    for i in range(n_pos-1, len(neg)):
        operations.append((tmp, neg[i]))
        tmp = tmp - neg[i]
else:
    neg = A[:N//2]
    pos = A[N//2:]
    if N % 2 == 1:
        tmp = pos[0]
        for i in range(N//2):
            operations.append((neg[i], tmp))
            tmp = neg[i] - tmp
            operations.append((pos[i+1], tmp))
            tmp = pos[i+1] - tmp
    else:
        operations.append(pos[0], neg[0])
        tmp = pos[0] - neg[0]
        if i in range(1, N//2):
            operations.append(neg[i], tmp)
            tmp = neg[i] - tmp
            operations.append(pos[i], tmp)
            tmp = pos[i] - tmp

print(tmp)
for o in operations:
    print("{} {}".format(o[0], o[1]))