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: Time Limit Exceeded)

def key_gen(i, j):
    return tuple([k for k in range(i, j + 1)])


def sub(A, D):
    A.sort()
    N = len(A)
    for i in range(N):
        key = key_gen(i, i)
        D[key] = (A[i], None), (A[i], None)
    for l in range(2, N + 1):
        for i in range(N - l + 1):
            j = i + l - 1
            key = key_gen(i, j)
            min_sub_list = []
            max_sub_list = []
            # lowest
            key_i = list(key)
            index = key_i.pop(0)
            ikey = tuple(key_i)
            res_min_i, res_max_i = D[ikey]
            a_i = A[index]
            b_i_min, pair_i_min = res_min_i
            b_i_max, pair_i_max = res_max_i
            min_sub_list.append((-abs(a_i - b_i_min), (a_i, b_i_min, pair_i_min)))
            min_sub_list.append((-abs(a_i - b_i_max), (a_i, b_i_max, pair_i_max)))
            max_sub_list.append((abs(a_i - b_i_min), (a_i, b_i_min, pair_i_min)))
            max_sub_list.append((abs(a_i - b_i_max), (a_i, b_i_max, pair_i_max)))
            # highest
            key_i = list(key)
            index = key_i.pop(-1)
            ikey = tuple(key_i)
            res_min_i, res_max_i = D[ikey]
            a_i = A[index]
            b_i_min, pair_i_min = res_min_i
            b_i_max, pair_i_max = res_max_i
            min_sub_list.append((-abs(a_i - b_i_min), (a_i, b_i_min, pair_i_min)))
            min_sub_list.append((-abs(a_i - b_i_max), (a_i, b_i_max, pair_i_max)))
            max_sub_list.append((abs(a_i - b_i_min), (a_i, b_i_min, pair_i_min)))
            max_sub_list.append((abs(a_i - b_i_max), (a_i, b_i_max, pair_i_max)))
            res_min = min(min_sub_list)
            res_max = max(max_sub_list)
            D[key] = res_min, res_max


def pair_extract(p, pair_list):
    while p is not None:
        a = p[0]
        b = p[1]
        p_next = p[2]
        pair_list.append((a, b))
        p = p_next


N = int(input())
A_temp = map(int, input().split())
A = list(A_temp)
D = {}
sub(A, D)
res_max = D[tuple([i for i in range(len(A))])][1]
max_val = res_max[0]
pair_list = []
pair_extract(res_max[1], pair_list)
pair_list.reverse()
print(max_val)
for p in pair_list:
    print(p[0], p[1])