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)

// Reads multiple ints in a line, separate by a space.
// It works even if the actual number of ints is smaller than n.
// WARNING: This function does not work for -2^31.
// NOTE: This function does not handle error cases.
fun fastReadInts(n: Int): IntArray {
    val xs = IntArray(n)
    val s = readLine()!!
    var currentValue = 0
    var isNegative = false
    var currentIndex = 0
    for (c in s) {
        if (c == ' ') {
            xs[currentIndex] = currentValue * if (isNegative) -1 else 1
            currentValue = 0
            isNegative = false
            currentIndex++
        } else if (c == '-') {
            isNegative = true
        } else {
            currentValue *= 10
            currentValue += c - '0'
        }
    }
    xs[currentIndex] = currentValue * if (isNegative) -1 else 1
    return xs
}

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val xs = fastReadInts(n)
    xs.sortDescending()

    val output = StringBuilder()
    if (xs.all { it >= 0 }) {
        for (i in 1..(n - 2)) {
            output.append("${xs[n - 1]} ${xs[i]}\n")
            xs[n - 1] = xs[n - 1] - xs[i]
        }
        output.append("${xs[0]} ${xs[n - 1]}\n")
        xs[0] = xs[0] - xs[n - 1]
        println(xs[0])
        print(output)
    } else if (xs.all { it < 0 }) {
        for (i in 1..(n - 1)) {
            output.append("${xs[0]} ${xs[i]}\n")
            xs[0] = xs[0] - xs[i]
        }
        println(xs[0])
        print(output)
    } else {
        val firstNegativeIndex = xs.indexOfFirst { it < 0 }
        for (i in 1 until firstNegativeIndex) {
            output.append("${xs[n - 1]} ${xs[i]}\n")
            xs[n - 1] = xs[n - 1] - xs[i]
        }
        for (i in firstNegativeIndex until n) {
            output.append("${xs[0]} ${xs[i]}\n")
            xs[0] = xs[0] - xs[i]
        }
        println(xs[0])
        print(output)
    }
}