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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const int N = 1e5 + 5;
int a[N];

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n;
    cin >> n;

    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }

    sort(a, a + n);

    int ans = a[n - 1] - a[0];

    for (int i = 1; i + 1 < n; i++) {
        ans += abs(a[i]);
    }

    cout << ans << "\n";

    int anime = a[0];

    for (int i = 1; i + 1 < n; i++) {
        if (a[i] > 0) {
            cout << anime << " " << a[i] << "\n";
            anime -= a[i];
        }
    }

    cout << a[n - 1] << " " << anime << "\n";

    anime = a[n - 1] - anime;

    for (int i = 1; i + 1 < n; i++) {
        if (a[i] <= 0) {
            cout << anime << " " << a[i] << "\n";
            anime -= a[i];
        }
    }

    return 0;
}