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 (1.15.1) (judge verdict: Accepted)

#[test]
fn check_solve() {
    println!("input:\n3\n1 -1 2\noutput:\n{}\n", solve("3\n1 -1 2\n"));
    println!("input:\n3\n1 1 1\noutput:\n{}\n", solve("3\n1 1 1\n"));
    println!(
        "input:\n5\n-2 -1 0 1 2\noutput:\n{}\n",
        solve("5\n-2 -1 0 1 2\n")
    );
    println!(
        "input:\n5\n1 2 3 4 5\noutput:\n{}\n",
        solve("5\n1 2 3 4 5\n")
    );
    println!(
        "input:\n5\n-5 -4 -3 -2 -1\noutput:\n{}\n",
        solve("5\n-5 -4 -3 -2 -1\n")
    );
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);
    let mut ret = String::new();
    use std::fmt::Write;
    let n: usize = sc.read();
    let mut a: Vec<isize> = (0..n).map(|_| sc.read()).collect();
    a.sort();
    let mut k = 1;
    while k < n - 1 && a[k] < 0 {
        k += 1;
    }
    for i in k..n - 1 {
        writeln!(&mut ret, "{} {}", a[0], a[i]).unwrap();
        a[0] -= a[i];
    }
    for i in 0..k {
        writeln!(&mut ret, "{} {}", a[n - 1], a[i]).unwrap();
        a[n - 1] -= a[i];
    }

    format!("{}\n{}", a[n - 1], ret)
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}