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(non_snake_case)]

use std::io::{stdin, Read};
use std::str::FromStr;
fn read_option<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok()
}
fn read<T: FromStr>() -> T {
    let opt = read_option();
    opt.expect("failed to parse token")
}

fn main() {
    let N: usize = read();
    let vec: Vec<isize> = (0..N).map(|_| read()).collect();
    let ans = solve(vec);
    println!("{}", ans.0);
    for v in ans.1 {
        println!("{} {}", v.0, v.1);
    }
}

fn solve(seq: Vec<isize>) -> (usize, Vec<(isize, isize)>) {
    let mut ans = vec![];
    let mut minuses = vec![];
    let mut pluses = vec![];
    let mut zeros = vec![];
    for v in seq {
        match v {
            0 => zeros.push(0),
            a if a < 0 => minuses.push(a),
            a if a > 0 => pluses.push(a),
            _ => panic!(),
        }
    }
    minuses.sort();
    pluses.sort();
    pluses.reverse();

    loop {
        match (zeros.len(), pluses.len(), minuses.len()) {
            (1, 0, 0) | (0, 1, 0) | (0, 0, 1) => break,
            (0, 1, _) => {
                let minus = minuses.pop().unwrap();
                let plus = pluses.pop().unwrap();
                ans.push((plus, minus));
                pluses.push(plus - minus);
            }
            (0, _, 1) => {
                let minus = minuses.pop().unwrap();
                let plus = pluses.pop().unwrap();
                ans.push((minus, plus));
                minuses.push(minus - plus);
            }
            // all minus
            (0, 0, _) => {
                let minus_1 = minuses.pop().unwrap();
                let minus_2 = minuses.pop().unwrap();
                ans.push((minus_1, minus_2));
                pluses.push(minus_1 - minus_2);
            }
            // all plus
            (0, _, 0) => {
                let plus_1 = pluses.pop().unwrap();
                let plus_2 = pluses.pop().unwrap();
                ans.push((plus_1, plus_2));
                minuses.push(plus_1 - plus_2);
            }
            (0, plus_count, minus_count) => {
                let minus = minuses.pop().unwrap();
                let plus = pluses.pop().unwrap();
                if plus_count >= minus_count {
                    ans.push((plus, minus));
                    pluses.push(plus - minus);
                } else {
                    ans.push((minus, plus));
                    minuses.push(minus - plus);
                }
            }
            (1, _, 0) => {
                let plus = pluses.pop().unwrap();
                let zero = zeros.pop().unwrap();
                ans.push((zero, plus));
                minuses.push(-plus);
            }
            (1, 0, _) => {
                let minus = minuses.pop().unwrap();
                let zero = zeros.pop().unwrap();
                ans.push((zero, minus));
                pluses.push(-minus);
            }
            (1, _, _) => {
                let plus = pluses.pop().unwrap();
                let zero = zeros.pop().unwrap();
                ans.push((plus, zero));
                pluses.push(plus);
            }
            (_, _, _) => {
                let zero_1 = zeros.pop().unwrap();
                let zero_2 = zeros.pop().unwrap();
                ans.push((zero_1, zero_2));
                zeros.push(0);
            }
        }
    }
    if pluses.is_empty() {
        (0, ans)
    } else {
        (pluses[0] as usize, ans)
    }
}