Problem:
Score : 400 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, arranged in a row in this order.

You can perform the following operation on this integer sequence any number of times:

Operation: Choose an integer i satisfying 1 \leq i \leq N-1. Multiply both A_i and A_{i+1} by -1.

Let B_1, B_2, ..., B_N be the integer sequence after your operations.

Find the maximum possible value of B_1 + B_2 + ... + B_N.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

-10^9 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value of B_1 + B_2 + ... + B_N.

Sample Input 1

3
-10 5 -4

Sample Output 1

19

If we perform the operation as follows:

Choose 1 as i, which changes the sequence to 10, -5, -4.

Choose 2 as i, which changes the sequence to 10, 5, 4.

we have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.

Sample Input 2

5
10 -4 -8 -11 3

Sample Output 2

30

Sample Input 3

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000

Sample Output 3

10000000000

The output may not fit into a 32-bit integer type.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

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

func main() {
	N := nextInt()
	as := make([]int, N)
	for i := 0; i < N; i++ {
		as[i] = nextInt()
	}

	var sum int
	for i := 0; i < N-1; i++ {
		if as[i] < 0 {
			if as[i+1] < 0 || abs(as[i]) >= abs(as[i+1]) {
				as[i] *= -1
				as[i+1] *= -1
			}
		}

		sum += as[i]
	}

	fmt.Println(sum + as[N-1])
}

// Input. ----------

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Buffer([]byte{}, math.MaxInt64)
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}

	return i
}

func nextFloat() float64 {
	sc.Scan()
	f64, err := strconv.ParseFloat(sc.Text(), 64)
	if err != nil {
		panic(err)
	}

	return f64
}

func nextString() string {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}

	return sc.Text()
}

// ---------- Input.

// Util. ----------

func abs(x int) int {
	return int(math.Abs(float64(x)))
}

func min(x, y int) int {
	return int(math.Min(float64(x), float64(y)))
}

func max(x, y int) int {
	return int(math.Max(float64(x), float64(y)))
}

// ---------- Util.