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: Wrong Answer)

fun main(args: Array<String>) {
    val n = Integer.parseInt(readInputLine())
    var a: MutableList<Long> = mutableListOf()
    
    val inputs = readInputLine().split(" ").map { it.toLong() }
    for (i in 0 until n) {
        a.add(inputs[i])
    }

    a.sort()
    
    val b: MutableList<Pair<Long, Long>> = mutableListOf()
    
    while (a.size != 2) {
        val x = a.removeAt(0)
        val y = a.removeAt(a.size - 2)
        a.add(0, x - y)
        b.add(Pair(x, y))
    }
    
    b.add(Pair(a[1], a[0]))
    
    println("${a[1] - a[0]}")
    
    for (elem in b) {
        println("${elem.first} ${elem.second}")
    }
}
 
fun readInputLine(): String {
    return readLine()!!
}