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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

public static partial class Program
{
    public static void Main()
    {
        var n = CRL().ToInt();
        var ais = CRL().ArrayLongs();
        var flag = ais.Count(x => x < 0).IsEven();
        var sum = ais.Sum(x => Math.Abs(x));
        CWL(sum - (flag ? 0 : ais.Min(x => Math.Abs(x)) * 2));
    }
}

public static partial class Program
{
    //テンプレここから
    public static long GCD(long a, long b) => b == 0 ? a : GCD(b, a % b);
    public static int GCD(int a, int b) => b == 0 ? a : GCD(b, a % b);
    public static long LCM(long a, long b) => a * b / GCD(a, b);
    public static int LCM(int a, int b) => a * b / GCD(a, b);
    public static int ToInt(this double d) => (int) d;
    public static long ToLong(this double d) => (long) d;
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] ToInt(this IEnumerable<string> strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static int[] ArrayInts(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static string CRL() => Console.ReadLine();
    public static string RL() => ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static void WL(object obj) => WriteLine(obj);
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static int Diff(int a, int b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static long Sign(this long i) => Math.Sign(i);
    public static bool IsEven(this long i) => i % 2 == 0;
    public static bool IsEven(this int i) => i % 2 == 0;
    public static long[] dx = new long[] {0, -1, 0, 1};
    public static long[] dy = new long[] {-1, 0, 1, 0};
    public static long mod = 1000000007;
    public static string alphabet = "abcdefghijklmnopqrstuvwxyz";
    public static long ToLong(this char c) => c.ToString().ToInt();
    public static long[] Sort(this long[] array) => array.OrderBy(x => x).ToArray();
    public static int[] Sort(this int[] array) => array.OrderBy(x => x).ToArray();
    public static long[] DSort(this long[] array) => array.OrderByDescending(x => x).ToArray();
    public static int[] DSort(this int[] array) => array.OrderByDescending(x => x).ToArray();
    public static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);

    public static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);

    //テンプレここまで
}