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)

# coding: utf-8
n = int(input())
a = list(map(int, input().split()))
#print(n, a)

print_list = []
    
pos = [x for x in a if x>=0]
neg = [x for x in a if x<0]
#print(pos, neg)
while(len(pos) != len(neg)):
    if len(pos) == 0:
        x = max(neg)
        y = min(neg)
        z = x - y
        neg.remove(x)
        neg.remove(y)
        pos.append(z)
        print_list.append((x, y))
    elif len(neg) == 0:
        x = min(pos)
        y = max(pos)
        z = x - y
        pos.remove(x)
        pos.remove(y)
        neg.append(z)
        print_list.append((x, y))
    elif len(pos) < len(neg):
        x = max(pos)
        y = min(neg)
        z = x - y
        pos.remove(x)
        neg.remove(y)
        pos.append(z)
    elif len(pos) > len(neg):
        x = min(neg)
        y = max(pos)
        z = x - y 
        neg.remove(x)
        pos.remove(y)
        neg.append(z)
        print_list.append((x, y))
    else:
        pass
# len(pos) == len(neg)
while(True):
    tmp_pos, tmp_neg = [], []
    if len(pos) == 1 and len(neg) == 1:
        x = max(pos)
        y = min(neg)
        z = x - y
        print_list.append((x, y))
        break
    elif len(pos)%2 == 0:
        for i in range(len(pos)):
            if i % 2 == 0:
                x, y = pos[i], neg[i]
                z = x - y
                tmp_pos.append(z)
                print_list.append((x, y))
            else:
                x, y = neg[i], pos[i]
                z = x - y
                print_list.appen((x, y))
                tmp_neg.append(z)
        pos = tmp_pos
        neg = tmp_neg
    else:
        for i in range(len(pos)-1):
            if i % 2 == 0:
                x, y = pos[i], neg[i]
                z = x - y
                print_list.append((x, y))
                tmp_pos.append(z)
            else:
                x, y = neg[i], pos[i]
                z = x - y
                print_list.append((x, y))
                tmp_neg.append(z)
        tmp_pos.append(pos[i+1])
        tmp_neg.append(neg[i+1])
        pos = tmp_pos
        neg = tmp_neg
            
            
print(z)
for i in range(len(print_list)):
    x = print_list[i][0]
    y = print_list[i][1]
    print(x, y)