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: Runtime Error)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;
use std::collections::VecDeque;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()

}

fn main(){
    let n: usize = read_as_vec()[0];

    let mut a: Vec<i64> = read_as_vec();

    let mut a = a.into_iter().filter(|x| *x != 0).collect::<Vec<i64>>();
    a.sort();
    let mut minus_counter = a.iter().filter(|x| **x < 0).count();
    let mut plus_counter = n  - minus_counter;

    let mut a_deque = VecDeque::new();

    for elem in a{
        a_deque.push_back(elem);
    }
    let mut a = a_deque;
    
    let mut ops: Vec<(i64, i64)> = Vec::new();
    
    if minus_counter == 0{
        let front = a.pop_front().unwrap();
        let back = a.pop_back().unwrap();
        ops.push((front, back));
        a.push_front(front - back);
        minus_counter += 1;
        plus_counter -= 2;
    }else if plus_counter == 0{
        let front = a.pop_front().unwrap();
        let back = a.pop_back().unwrap();
        ops.push((back, front));
        a.push_back(back - front);
        minus_counter -= 2;
        plus_counter += 1;        
    }

    while a.len() > 2{
        let front = a.pop_front().unwrap();
        let back = a.pop_back().unwrap();
        if minus_counter == 1{
            a.push_front(front - back);
            ops.push((front, back));
            plus_counter -= 1;
        }else{
            a.push_back(back - front);
            ops.push((back, front));
            minus_counter -= 1;
        }
    }
    
    let front = a.pop_front().unwrap();
    let back = a.pop_back().unwrap();
    a.push_back(back-front);
    ops.push((back, front));
    println!("{}", a[0].abs());
    for op in ops{
        println!("{} {}", op.0, op.1);
    }
}