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: Wrong Answer)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};

#[allow(unused_imports)]
use std::io::Write;

fn main() {
    input!{
      n: usize,
      mut aa: [i64; n],
    }
    let mut ps = vec![];
    let mut ms = vec![];
    for i in 0..n {
        if aa[i] >= 0 {
            ps.push(aa[i]);
        } else {
            ms.push(aa[i]);
        }
    }
    ps.sort();
    ms.sort();

    if ps.len() >= ms.len() {
        let t = ps.len() - ms.len();
        let mut pairs = std::collections::VecDeque::new();
        for i in 0..t/2 {
            let a = ps[i];
            let b = ps[t - i - 1];
            pairs.push_back((a, b));
        }

        let mut cmd = vec![];
        let mut cur = 0 as i64;
        if t > 0 {
            if t%2 == 0 {
                let (a, b) = pairs.pop_back().unwrap();
                cur = (b-a);
                cmd.push((b, a));
            } else {
                cur = ps[ (t/2) as usize ];
                debug!(ps, t, cur);
            }
        }

        for &(a, b) in pairs.iter() {
            cmd.push((a, b));
            cmd.push((cur, a-b));
            cur -= (a-b);
        }

        // lenが一緒
        for i in 0..ms.len() {
            let a = ps[i+t];
            let b = ms[i];
            if t == 0 && i == 0 {
                cmd.push((a, b));
                cur = a-b;
            } else {
                cmd.push((b, a));
                cmd.push((cur, b-a));
                cur -= (b-a);
            }
        }

        println!("{}", cur);
        for (a, b) in cmd {
            println!("{} {}", a, b);
        }
    } else {
        let t = ms.len() - ps.len();
        ms.reverse();
        let mut cur = ms[0];
        let mut cmd = vec![];

        for i in 1..t {
            cmd.push((cur, ms[i]));
            cur -= ms[i];
        }

        for i in 0..ps.len() {
            let a = ps[i];
            let b = ms[i+t];
            cmd.push((b, a));
            cmd.push((cur, b-a));
            cur -= (b-a);
        }

        println!("{}", cur);
        for (a, b) in cmd {
            println!("{} {}", a, b);
        }
    }
}