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())
lists=list(map(int,input().split()))

mini=min(lists)
maxi=max(lists)

if mini>=0 or maxi<=0:
    
    lists=sorted(lists)
    ans=0
    length=len(lists)//2
    
    for i in range(len(lists)):
        if i<=length-1:
            ans-=lists[i]
        else:
            ans+=lists[i]
    print(ans)
    
    some=lists[-1]
    
    if len(lists)%2!=0:
        some=lists[length]
        print(lists[0],some)
        some=lists[0]-some
        for i in range(1,length):
            print(lists[i+length],some)
            some=lists[i+length]-some
            print(lists[i],some)
            some=lists[i]-some
        print(lists[-1],some)

        
    elif len(lists)%2==0:
        some=lists[length]
        print(lists[0],some)
        some=lists[0]-some
        for i in range(1,length-1):
            print(lists[i+length],some)
            some=lists[i+length]-some
            print(lists[i],some)
            some=lists[i]-some
        print(lists[-1],some)
        some=lists[-1]-some
        print(some,lists[length-1])
        some=some-lists[length-1]


else:
    lists=sorted(lists)
    positive=0
    negative=0
    zero=0
    
    for some in lists:
        if some >0:
            positive+=1  
        elif some==0:
            zero+=1 
        elif some<0:
            negative+=1
    ans=0
    if negative>positive:

        z=0
        for _ in  lists:
            z+=abs(_)
        print(z)
        #解答の出力
        ans=lists[-1]
        for i in range(negative-positive):
            print(ans,lists[i])
            ans=ans-lists[i]
        x=negative-positive
        for j in range(positive-1):
            print(ans,lists[x+j])
            ans=ans-lists[x+j]
            print(lists[x+j+1],ans)
            ans=lists[x+j+1]-ans

        print(lists[-negative],ans)
        for i in range(zero):
            print(z,0)

    elif negative<positive:
        z=0
        for _ in  lists:
            z+=abs(_)
        print(z)
        #解答の出力        
        ans=lists[0]
        for i in range(1,positive-negative+1):
            print(ans,lists[-i])
            ans=ans-lists[-i]
        x=positive-negative+1
        for i in range(negative-1):
            print(lists[-x-i],ans)
            ans=lists[-x-i]-ans
            print(lists[i+1],ans)  
            ans=lists[i+1]-ans
        print(lists[-positive],ans)
        for i in range(zero):
            print(z,0)
    else:   
        
        ans=0
        length=len(lists)//2
    
        for i in range(len(lists)):
            if i<=length-1:
                ans-=lists[i]
            else:
                ans+=lists[i]
        print(ans) 
        
        ans=lists[0]
        for j in range(1,positive):
            print(lists[-j],ans)
            ans=lists[-j]-ans
            print(lists[j],ans)
            ans=lists[j]-ans    
        print(lists[positive],ans)
        for i in range(zero):
            print(z,0)