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 Rust (1.42.0) (judge verdict: Accepted)

use std::cmp;
use std::fmt::Debug;
use std::str::FromStr;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where
    T: FromStr,
    <T as FromStr>::Err: Debug,
{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim()
        .split_whitespace()
        .map(|c| T::from_str(c).unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_as_string() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[test]
fn test_random() {
    assert_eq!(2 + 2, 4);
}

fn main() {
    let n = read_as_vec::<usize>()[0];
    let mut a = read_as_vec::<i64>();
    let mut steps: Vec<(i64, i64)> = vec![];
    a.sort();
    // maybe minus if given all numbers are minus.
    let mut only_plus_number = a.pop().unwrap();
    let mut minus_numbers: Vec<i64> = vec![];
    let mut plus_numbers: Vec<i64> = vec![];
    a.reverse();
    minus_numbers.push(a.pop().unwrap());
    for elem in a {
        if 0 <= elem {
            plus_numbers.push(elem);
        } else {
            minus_numbers.push(elem);
        }
    }

    while let Some(y) = plus_numbers.pop() {
        let x = minus_numbers.pop().unwrap();
        steps.push((x, y));
        minus_numbers.push(x - y);
    }

    for minus_number in minus_numbers {
        steps.push((only_plus_number, minus_number));
        only_plus_number -= minus_number;
    }

    println!("{}", only_plus_number);
    for step in steps {
        println!("{} {}", step.0, step.1);
    }
}