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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.ArrayDeque
import java.math.*

fun main(args: Array<String>) {
    val N = readInputLine().toInt()
    val AList = readInputLine().split(" ").map { it.toInt() }.sorted()
    val absSum = AList.sumBy { Math.abs(it) }
    val deque = ArrayDeque<Int>(N)
    
    for (a in AList) {
        deque.addLast(a)
    }
    
    val first = deque.peekFirst()
    val last = deque.peekLast()
    
    if (last < 0) {
        println(absSum - last * -2)
        println("$last $first")
        deque.pollFirst()
        deque.pollLast()
        deque.addLast(last - first)
    } else if (first > 0) {
        println(absSum - first * 2)
        println("$first $last")
        deque.pollFirst()
        deque.pollLast()
        deque.addFirst(first - last)
    } else {
        println(absSum)
    }
    
    if (deque.size == 1) {
        return
    }
    
    while (deque.size > 2) {
        val first = deque.pollFirst()
        val last = deque.pollLast()
        
        if (deque.peekFirst() >= 0) {
            println("$first $last")
            deque.addFirst(first - last)
        } else {
            println("$last $first")
            deque.addLast(last - first)
        }
    }
    
    println("${deque.pollLast()} ${deque.pollLast()}")
}

fun readInputLine(): String {
    return readLine()!!
}