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)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize,
        a: [i64; n]
    }

    let mut plus = Vec::new();
    let mut minus = Vec::new();
    let mut zeros = Vec::new();
    for v in a {
        match v.cmp(&0) {
            Ordering::Less => minus.push(v),
            Ordering::Equal => zeros.push(v),
            Ordering::Greater => plus.push(v),
        }
    }
    plus.sort();
    minus.sort();
    minus.reverse();
    let mut opes = Vec::new();
    if plus.is_empty() {
        zeros.append(&mut minus);
        minus = zeros;
        let mut prev = minus[0];
        for &v in minus.iter().skip(1) {
            opes.push((prev, v));
            prev -= v;
        }
    } else if minus.is_empty() {
        zeros.append(&mut plus);
        plus = zeros;
        let mut prev = plus[0];
        for &v in plus.iter().take(plus.len() - 1).skip(1) {
            opes.push((prev, v));
            prev -= v;
        }
        opes.push((*plus.last().unwrap(), prev));
    } else {
        zeros.append(&mut minus);
        minus = zeros;
        let mut prev = minus[0];
        for &v in plus.iter().take(plus.len() - 1) {
            opes.push((prev, v));
            prev -= v;
        }
            opes.push((*plus.last().unwrap(), prev));
            prev = *plus.last().unwrap() - prev;
        for &v in minus.iter().skip(1) {
            opes.push((prev, v));
            prev -= v;
        }
    }

    let (x, y) = *opes.last().unwrap();
    println!("{}", x - y);
    for (x, y) in opes {
        println!("{} {}", x, y);
    }
}