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 = list(map(int, input().split()))
P = []
M = []
for a in A:
    if a >= 0:
        P.append(a)
    else:
        M.append(a)

P.sort(reverse=True)
M.sort()
if N % 2 == 0:
    if len(P) > N // 2:
        M += P[N // 2:]
        M.sort(reverse=True)
        P = P[:N // 2]
        P.sort()
    else:
        P += M[N // 2:]
        P.sort()
        M = M[:N // 2]
        M.sort(reverse=True)
    x = 0
    y = 0
    print(sum(P)-sum(M))
    for i in range(N - 1):
        if i % 2 == 0:
            y = x-y if i!=0 else M[0]
            x = P[i // 2]
        else:
            y = x - y
            x = M[i//2+1]
        print(x,y)
else:
    # Pの方を1つ増やすパターン
    if len(P) > N // 2:
        M += P[N // 2+1:]
        M.sort(reverse=True)
        P = P[:N // 2+1]
        P.sort()
    else:
        P += M[N // 2+1:]
        P.sort()
        M = M[:N // 2+1]
        M.sort(reverse=True)
    x = 0
    y = 0
    print(sum(P)-sum(M))
    if len(P) > len(M):
        for i in range(N - 1):
            if i % 2 == 0:
                y = x-y if i!=0 else P[0]
                x = M[i // 2]
            else:
                y = x - y
                x = P[i//2+1]
            print(x, y)
    else:
        for i in range(N - 1):
            if i % 2 == 0:
                x = x - y if i != 0 else M[0]
                y = P[i // 2]
            else:
                x = x - y
                y = M[i // 2 + 1]
            print(x,y)