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)

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let mut a: Vec<i64> = sc.vec(n);

    if a.iter().all(|&a| a >= 0) {
        a.sort();
        let mut ans = vec![];
        let mut cur = a[0];
        for i in 1..(n - 1) {
            ans.push((cur, a[i]));
            cur -= a[i];
        }
        ans.push((a[n - 1], cur));
        let m = a[n - 1] - cur;
        sc.write(format!("{}\n", m));
        for (x, y) in ans.into_iter() {
            sc.write(format!("{} {}\n", x, y));
        }
    } else if a.iter().all(|&a| a <= 0) {
        a.sort();
        a.reverse();
        let mut cur = a[0];
        let mut ans = vec![];
        for i in 1..n {
            ans.push((cur, a[i]));
            cur -= a[i];
        }
        sc.write(format!("{}\n", cur));
        for (x, y) in ans.into_iter() {
            sc.write(format!("{} {}\n", x, y));
        }
    } else {
        let mut negative = vec![];
        let mut non_negative = vec![];
        for a in a.into_iter() {
            if a < 0 {
                negative.push(a);
            } else {
                non_negative.push(a);
            }
        }
        let mut positive = non_negative.pop().unwrap();
        let mut cur = negative.pop().unwrap();
        let mut ans = vec![];
        for non_negative in non_negative.into_iter() {
            ans.push((cur, non_negative));
            cur -= non_negative;
        }
        for negative in negative.into_iter() {
            ans.push((positive, negative));
            positive -= negative;
        }
        ans.push((positive, cur));
        positive -= cur;

        sc.write(format!("{}\n", positive));
        for (x, y) in ans.into_iter() {
            sc.write(format!("{} {}\n", x, y));
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}