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_imports)]
#![allow(non_snake_case)]
use std::io::Read;
use std::io::{stdout, BufWriter, Write};
 
fn main() {
    let mut buf = String::new();
    
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
 
    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();
 
    // 読み込んだStringを空白で分解する
    let mut iter = buf.split_whitespace();
 
    //let mut a = [[0i64; 100]; 50];
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    //let k: i64 = iter.next().unwrap().parse().unwrap();
    
    let mut v = (0..n).map(|_|{
        iter.next().unwrap().parse().unwrap()
    }).collect::<Vec<i64>>();
    
    v.sort();
    
    let mut minus = 0;
    for i in 0..n{
        if v[i] < 0 {
            minus += 1;
        }
    }
    
    //println!("minus : {}",minus);
    
    if n == 2{
        println!("{}", v[1] - v[0]);
        println!("{} {}", v[1] , v[0]);
        return;
    }
    
    let mut sum = 0;
    
    for i in 1..n-1 {
        //sum += v[i];
        if i < minus {
            sum -= v[i];
        }
        else{
            sum += v[i];
        }
    }
    
    sum = sum + v[n-1] - v[0];
    
    println!("{:?}", sum);
    
    let mut tmp = v[0];
    let mut first_index = minus;
    if first_index == 0 {
        first_index = 1;
    }
    
    
    for i in first_index..n-1 {
        println!("{} {}", tmp, v[i]);
        tmp = tmp - v[i];
    }
    
    println!("{} {}", v[n-1], tmp);
    tmp = v[n-1] - tmp;
    
    for i in 1..minus {
        println!("{} {}", tmp, v[i]);
        tmp = tmp - v[i];
    }
    
    //println!("{:?}", v);
    
}