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 sol():
    n=int(input())
    #n,k=map(int,input().split())
    l=[int(i) for i in input().split()]
    a=[(abs(l[i]),i) for i in range(n)]
    x=l[a[0][1]]
    d=[]
    for i in range(1,n):
        y=l[a[i][1]]
        #d.append((max(x,y),min(x,y)))
        d.append((min(x,y),max(x,y)))
        #x=max(x,y)-min(x,y)
        x=min(x,y)-max(x,y)
        #if x<y:
        #    d.append((x,y))
        #    x=x-y
        #else:
        #    d.append((y,x))
        #    x=(y-x)
    #print(d)
    print(abs(d[-1][0]-d[-1][1]))
    for x,i in enumerate(d):
        if x+1==n-1:
            print(max(i),min(i))
        else:
            print(i[0],i[1])

if __name__=="__main__":
    sol()