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: Wrong Answer)

using System;
using static System.Console;
using System.Text;
using System.Linq;
using static System.Math;
using System.Collections.Generic;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;

class Program
{
    public static int count = 0;
    static void Main(string[] args)
    {
        var alg = new cp();
        var n = alg.inputLong();
        //var s=inputString();
        var arr = alg.inputSplitLong();
        //var jug=inputJaggedArrayInt(n);
        long max = -1000000000000000;
        long maxIndex = 0;
        long minIndex = 0;
        long min = 10000000000000000;
        long minuscount = 0;
        for (long a = 0; a < n; a++)//マイナス符号をプラスに
        {
            if (arr[a] < 0) {
                max = Math.Max(max, arr[a]);
                maxIndex = a;
                arr[a] = arr[a] * -1;
                minuscount++;
            }
            else if(arr[a]>0)
            {
                minIndex = a;
                
                min = Math.Min(min,arr[a]);

            }

        }
        if (minuscount%2==1)
        {
            if (Math.Abs(arr[maxIndex])> Math.Abs(arr[minIndex]))
            {
                arr[minIndex] *= -1;
            }
            else if(Math.Abs(arr[maxIndex]) < Math.Abs(arr[minIndex]))
            {
                arr[minIndex] *= -1;
            }
            else
            {
                arr[maxIndex] *= -1;
            }
        }
        WriteLine(arr.Sum());
    }
}

class cp
{

    public cp()
    {
    }
    public int GCD(int a, int b)
    {
        return a % b == 0 ? b : GCD(b, a % b);
    }
    public int LCM(int a, int b)
    {
        return a * b / GCD(a, b);
    }
    public int countChar(string s, string key)
    {
        return s.Length - s.Replace(key, "").Length;
    }
    public string YesNo(bool f, string type = null)
    {
        string str;
        if (f) str = "Yes"; else str = "No";
        if (type == "lower") return str.ToLower(); else if (type == "upper") return str.ToUpper(); else return str;
    }
    public void inputSkip()
    {
        ReadLine();
        return;
    }
    public string inputString()
    {
        return ReadLine();
    }
    public string[] inputSplitString()
    {
        return ReadLine().Split();
    }
    public string[] inputLinesString(int len)
    {
        var arr = new string[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine();
        }
        return arr;
    }
    public string[][] inputJaggedArrayString(int len)
    {
        var arr = new string[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split();
        }
        return arr;
    }
    public int inputInt()
    {
        return int.Parse(ReadLine());
    }
    public int[] inputSplitInt()
    {
        return ReadLine().Split().Select(i => int.Parse(i)).ToArray();
    }
    public int[] inputLinesInt(int len)
    {
        var arr = new int[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = int.Parse(ReadLine());
        }
        return arr;
    }
    public int[][] inputJaggedArrayInt(int len)
    {
        var arr = new int[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => int.Parse(i)).ToArray();
        }
        return arr;
    }
    public long inputLong()
    {
        return long.Parse(ReadLine());
    }
    public long[] inputSplitLong()
    {
        return ReadLine().Split().Select(i => long.Parse(i)).ToArray();
    }
    public long[] inputLinesLong(int len)
    {
        var arr = new long[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = long.Parse(ReadLine());
        }
        return arr;
    }
    public long[][] inputJaggedArrayLong(int len)
    {
        var arr = new long[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => long.Parse(i)).ToArray();
        }
        return arr;
    }
    public double inputDouble()
    {
        return double.Parse(ReadLine());
    }
    public double[] inputSplitDouble()
    {
        return ReadLine().Split().Select(i => double.Parse(i)).ToArray();
    }
    public double[] inputLinesDouble(int len)
    {
        var arr = new double[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = double.Parse(ReadLine());
        }
        return arr;
    }
    public double[][] inputJaggedArrayDouble(int len)
    {
        var arr = new double[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => double.Parse(i)).ToArray();
        }
        return arr;
    }
}