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_mut)]
#![allow(non_snake_case)]
#![allow(unused_imports)]
use std::collections::HashSet;
use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::VecDeque;
use std::cmp::{max, min};
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

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

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

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

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

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

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

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
fn main() {
    input! {
        n: usize,
        a: [i64; n],
    }
    let mut b = a.clone();
    let mut c = VecDeque::new();
    b.sort();
    for i in b {
        c.push_back(i);
    }
    if n % 2 == 0 {
        for i in 0..n - 1 {
            if i % 2 == 0 {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_front(l - r);
                //println!("{} {}", l, r);
            } else {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_back(r - l);
                //println!("{} {}", r, l);
            }
        }
    } else {
        for i in 0..n - 1 {
            //println!("{:?}", c);
            if i % 2 == 1 {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_back(r - l);
                //println!("{} {}", r, l);
            } else {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_front(l - r);
                //println!("{} {}", l, r);
            }
        }
    }
    println!("{}", c[0]);

    let mut b = a.clone();
    let mut c = VecDeque::new();
    b.sort();
    for i in b {
        c.push_back(i);
    }
    if n % 2 == 0 {
        for i in 0..n - 1 {
            if i % 2 == 0 {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_front(l - r);
                println!("{} {}", l, r);
            } else {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_back(r - l);
                println!("{} {}", r, l);
            }
        }
    } else {
        for i in 0..n - 1 {
            //println!("{:?}", c);
            if i % 2 == 1 {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_back(r - l);
                println!("{} {}", r, l);
            } else {
                let l = c.pop_front().unwrap();
                let r = c.pop_back().unwrap();
                c.push_front(l - r);
                println!("{} {}", l, r);
            }
        }
    }
    //println!("{}", c[0]);
}