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)

#![allow(unused_imports)]

use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::iter::once;
#[cfg(debug_assertions)]
include! {"./debug.rs"}

#[cfg(not(debug_assertions))]
macro_rules! debug {
    ($($arg:expr),*) => {};
}

macro_rules! read {
    ([$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ([$t:ident]) =>
        (rl().split_whitespace().map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    (_, [$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!(_, [$t])).collect::<Vec<_>>());
    (_, [$t:ident]) =>
        (rl().split_whitespace().skip(1).map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    ($($t:ident),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ($t:ident) => (read_type!(rl(), $t));
    ($($t:ident),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(read_type!(w.next().unwrap(), $t)),*)
    }};
}

macro_rules! read_type {
    ($s:expr, chars) => {
        $s.chars().collect::<Vec<char>>()
    };
    ($s:expr, usize1) => {
        read_type!($s, usize) - 1
    };
    ($s:expr, $t:ty) => {
        $s.parse::<$t>().unwrap()
    };
}

fn rl() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_owned()
}

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

////////////////////////////////////////////////////////////////////////////////

fn main() {
    let n = read!(usize);
    let mut a = read!([i64]);

    a.sort();

    let neg = a.iter().filter(|&&x| x <= 0).map(|&x| x).vec();
    let pos = a.iter().filter(|&&x| x > 0).map(|&x| x).vec();
    debug!(neg, pos);

    let mut ops = vec![];
    let mut ans: i64;

    if neg.len() > 0 && pos.len() > 0 {
        ans = neg[0];
        for i in 0..pos.len() - 1 {
            ops.push(format!("{} {}", ans, pos[i]));
            ans = ans - pos[i];
        }
        ops.push(format!("{} {}", pos[pos.len() - 1], ans));
        ans = pos[pos.len() - 1] - ans;
        for i in 1..neg.len() {
            ops.push(format!("{} {}", ans, neg[i]));
            ans = ans - neg[i];
        }
    } else if neg.len() == 0 {
        ans = pos[0];
        for i in 1..pos.len() - 1 {
            ops.push(format!("{} {}", ans, pos[i]));
            ans = ans - pos[i];
        }
        ops.push(format!("{} {}", pos[pos.len() - 1], ans));
        ans = pos[pos.len() - 1] - ans;
    } else {
        ans = neg[neg.len() - 1];
        for i in (0..neg.len() - 1).rev() {
            ops.push(format!("{} {}", ans, neg[i]));
            ans = ans - neg[i];
        }
    }

    println!("{}", ans);
    for s in ops {
        println!("{}", s);
    }
}