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>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

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

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
fn main() {
    input!{
        n: usize,
        a: [i64; n]
    }
    let mut nvec = vec![];
    let mut pvec = vec![];
    let mut sum = 0;
    for i in 0..n {
        sum+=a[i].abs();
        if a[i]>=0 {
            pvec.push(a[i]);
        }else{
            nvec.push(a[i]);
        }
    }
    pvec.sort();
    nvec.sort();
    nvec.reverse();
    // println!("{:?}", nvec);
    if nvec.len() >=1 && pvec.len() >=2{
        println!("{}", sum);
        println!("{} {}", nvec[0], pvec[0]);
        let mut dif = nvec[0] - pvec[0];
        for i in 1..(pvec.len() - 1) {
            println!("{} {}",  dif, pvec[i]);
            dif -=pvec[i];
        }
        println!("{} {}", pvec[pvec.len() - 1], dif);
        dif = pvec[pvec.len() - 1] - dif;
        for i in 1..nvec.len() {
            println!("{} {}", dif, nvec[i]);
            dif -=nvec[i];
        }
    }else if nvec.len() >=1 && pvec.len() ==1 {
        let mut dif = pvec[0] - nvec[0];
        println!("{}", sum);
        println!("{} {}", pvec[0], nvec[0]);
        for i in 1..nvec.len() {
            println!("{} {}", dif, nvec[i]);
            dif-=nvec[i];
        }
        // assert!(true);
    }else if nvec.len() >=1 && pvec.len() ==0 {
        let mut dif = nvec[0] - nvec[1];
        println!("{}", sum + nvec[0]*2);
        println!("{} {}", nvec[0], nvec[1]);
        for i in 2..nvec.len() {
            println!("{} {}", dif, nvec[i]);
            dif-=nvec[i];
        }
    }else{
        let mut dif = pvec[0] - pvec[1];
        println!("{}", sum - 2*pvec[0]);
        println!("{} {}", pvec[0], pvec[1]);
        for i in 2..(pvec.len()-1) {
            println!("{} {}", dif, pvec[i]);
            dif-=pvec[i];
        }
        println!("{} {}", pvec[pvec.len() - 1], dif);
    }
}