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: Time Limit Exceeded)

from bisect import bisect

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

ans = []

if len(A) == 2 :
    ans.append(A[::-1])
    calc = A[1] - A[0]

else :
    ind = bisect(A,0)

    X = A[:ind]
    Y = A[ind:]
    
    if len(X) == 0 :
        ans.append([Y[0],Y[1]])
        X.append(Y[0]-Y[1])
        Y.pop(0)
        Y.pop(0)
    elif len(Y) == 0 :
        ans.append([X[-1],X[-2]])
        Y.append(X[-1]-X[-2])
        X.pop(-1)
        X.pop(-1)
    
    while True :
        if len(X) >= 2 :
            ans.append([Y[0],X[-1]])
            Y[0] -= X.pop(-1)
        elif len(Y) >= 2 :
            ans.append([X[-1],Y[0]])
            X[-1] -= Y.pop(0)
        else :
            ans.append([Y[0],X[0]])
            calc = Y.pop(0) - X.pop(0)
            break
    
print(calc)
for i in range(len(ans)) :
    print(*ans[i])