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: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
)

func main() {
	io := NewIo()
	defer io.Flush()

	n := io.NextInt()

	nums := []int{}
	for i := 0; i < n; i++ {
		n := io.NextInt()
		nums = append(nums, n)
	}

	sort.Ints(nums)

	maxVal := nums[n-1]
	minVal := nums[0]
	nums = nums[1 : n-1]

	negaIdx := 0
	for negaIdx < n && nums[negaIdx] < 0 {
		negaIdx++
	}
	negatives := nums[:negaIdx]
	positives := []int{}
	if negaIdx < n {
		positives = nums[negaIdx:]
	}

	action := [][]int{}

	for _, v := range negatives {
		action = append(action, []int{maxVal, v})
		maxVal = maxVal - v
	}

	for _, v := range positives {
		action = append(action, []int{minVal, v})
		minVal = minVal - v
	}

	action = append(action, []int{maxVal, minVal})
	fmt.Println(maxVal - minVal)

	for _, v := range action {
		fmt.Println(v[0], v[1])
	}
}

type Io struct {
	reader    *bufio.Reader
	writer    *bufio.Writer
	tokens    []string
	nextToken int
}

func NewIo() *Io {
	return &Io{
		reader: bufio.NewReader(os.Stdin),
		writer: bufio.NewWriter(os.Stdout),
	}
}

func (io *Io) Flush() {
	err := io.writer.Flush()
	if err != nil {
		panic(err)
	}
}

func (io *Io) NextLine() string {
	var buffer []byte
	for {
		line, isPrefix, err := io.reader.ReadLine()
		if err != nil {
			panic(err)
		}
		buffer = append(buffer, line...)
		if !isPrefix {
			break
		}
	}
	return string(buffer)
}

func (io *Io) Next() string {
	for io.nextToken >= len(io.tokens) {
		line := io.NextLine()
		io.tokens = strings.Fields(line)
		io.nextToken = 0
	}
	r := io.tokens[io.nextToken]
	io.nextToken++
	return r
}

func (io *Io) NextInt() int {
	i, err := strconv.Atoi(io.Next())
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) NextFloat() float64 {
	i, err := strconv.ParseFloat(io.Next(), 64)
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) PrintLn(a ...interface{}) {
	fmt.Fprintln(io.writer, a...)
}

func (io *Io) Printf(format string, a ...interface{}) {
	fmt.Fprintf(io.writer, format, a...)
}

func (io *Io) PrintIntLn(a []int) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.PrintLn(b...)
}

func (io *Io) PrintStringLn(a []string) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.PrintLn(b...)
}

func Log(name string, value interface{}) {
	fmt.Fprintf(os.Stderr, "%s=%+v\n", name, value)
}

func abs(a int) int {
	if a >= 0 {
		return a
	} else {
		return -a
	}
}

func pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func strSearch(a []string, b string) bool {
	for i := 0; i < len(a); i++ {
		if a[i] == b {
			return true
		}
	}
	return false
}

func sortAsc(a []int) []int {
	sort.Ints(a)
	return a
}

func sortDesc(a []int) []int {
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
	return a
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

func lcm(a, b int) int {
	if a == 0 && b == 0 {
		return 0
	}
	return a * b / gcd(a, b)
}

func cumSum(nums []int) []int {
	sums := []int{0}

	for i := 0; i < len(nums); i++ {
		sums = append(sums, sums[i]+nums[i])
	}
	return sums
}