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 System.Collections.Generic;
using System.Linq;

namespace abc123
{
    class D
    {
        static void Main(string[] args)
        {
            int N = Input.Int();
            long[] A = Input.LongArray();

            long res = 0;

            for (int i = 0; i < N - 1; i++)
            {
                if (i < N - 2)
                {
                    if (A[i] < 0)
                    {
                        A[i + 1] *= -1;
                    }
                    res += Math.Abs(A[i]);
                }
                else
                {
                    if ((A[i] > 0 && A[i+1] > 0) || (A[i] < 0 && A[i+1] < 0))
                    {
                        res += Math.Abs(A[i]) + Math.Abs(A[i + 1]);
                    } else
                    {
                        if (Math.Abs(A[i]) > Math.Abs(A[i + 1])) {
                            res += Math.Abs(A[i]) + A[i + 1] * -1;
                        } else
                        {
                            res += Math.Abs(A[i + 1]) + A[i] * -1;
                        }
                        
                    }
                }
            }


            Console.WriteLine(res);

        }

        internal static class Input
        {
            public static int Int() => int.Parse(Console.ReadLine());

            public static string Str() => Console.ReadLine();

            public static int[] IntArray() => Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            public static long[] LongArray() => Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

        }
    }

    

}