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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)
	ar := make([]int, n)
	mi, pl := false, false
	for i := range ar {
		fmt.Scan(&ar[i])
		if ar[i] >= 0 {
			pl = true
		} else {
			mi = true
		}
	}
	sort.Ints(ar)
	if pl && mi {
		ans := 0
		for _, v := range ar {
			if v < 0 {
				ans -= v
			} else {
				ans += v
			}
			fmt.Println(ans)
		}
		plsum := ar[n-1]
		misum := ar[0]
		for i := 1; i < n-1; i++ {
			if ar[i] >= 0 {
				fmt.Println(misum, ar[i])
				misum -= ar[i]
			} else {
				fmt.Println(plsum, ar[i])
				plsum -= ar[i]
			}
		}
		fmt.Println(plsum, misum)
		return
	}
	if pl {
		ans := 0
		min := 999999
		for _, v := range ar {
			ans += v
			if v < min {
				min = v
			}
		}
		fmt.Println(ans - min*2)
		plsum := ar[n-1]
		misum := ar[0]
		for i := 1; i < n-1; i++ {
			fmt.Println(misum, ar[i])
			misum -= ar[i]
		}
		fmt.Println(plsum, misum)
		return
	}
	ans := 0
	min := 999999
	for _, v := range ar {
		ans -= v
		aa := -v
		if aa < min {
			min = aa
		}
	}
	fmt.Println(ans - min*2)
	misum := ar[n-1]
	for i := 0; i < n-1; i++ {
		fmt.Println(misum, ar[i])
		misum -= ar[i]
	}
	return
}