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)

N = int(input())
A = input().split()
A = [int(i) for i in A]

def positive_negative(target_list):
    positive = 0
    negative = 0
    zero = 0
    for i in target_list:
        if i > 0:
            positive = 1
        elif i < 0:
            negative = 1
        else:
            zero = 1
            
    if zero == 1:
        return 0
    elif positive == 1 and negative == 0:
        return 1
    elif positive == 1 and negative == 1:
        return 2
    else: # positive == 0 and negative == 1
        return 3
      
print_list = []

while(1):
    if len(A) == 2:
        break

    p_n = positive_negative(A)
    if p_n == 0:
        A.remove(0)
        A.append(A[0])
        print_list.append(str(A[0])+' '+str(0))
        A.remove(A[0])
    
    elif p_n == 1:
        min1 = min(A)
        A.remove(min1)
        min2 = min(A)
        A.remove(min2)
    
        print_list.append(str(min1)+' '+str(min2))
        A.append(min1 - min2)
    
    elif p_n == 2:
        min1 = min(A)
        A.remove(min1)
        max1 = max(A)
        A.remove(max1)
    
        print_list.append(str(min1)+' '+str(max1))
        A.append(min1 - max1)
    
    else: #p_n == 3
        min1 = min(A)
        A.remove(min1)
        max1 = max(A)
        A.remove(max1)

        print_list.append(str(max1)+' '+str(min1))
        A.append(max1 - min1)

min1 = min(A)
A.remove(min1)
max1 = max(A)
A.remove(max1)

print_list.append(str(max1)+' '+str(min1))
A.append(max1 - min1)


print(A[0])
for s in print_list:
    print(s)