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.Linq;
using System.Collections.Generic;

namespace ConsoleApp2
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int N;
            int[] listA;
            
            N = Read(Console.ReadLine())[0];
            int[] ansCollection = new int[N];
            listA = Read(Console.ReadLine());

            //find negative number
            int[] data = Negative_Min(listA);
            int negNum = data[0];
            int min = data[1];

            int ans = 0;

            if (negNum % 2 == 0)
            {
                foreach (var item in listA) ans += Math.Abs(item);
            }
            else
            {
                foreach (var item in listA) ans += Math.Abs(item);
                ans -= 2 * min;
            }
            Console.WriteLine(ans);

        }


        public static int[] Negative_Min(int[] array)
        {
            int neg = 0;
            int min = Math.Abs(array[0]);

            foreach (var num in array) 
            {
                if (num < 0) neg++;
                int ab = Math.Abs(num);
                if (min > ab) min = ab;
            }
            int[] ans = new int[2] { neg, min };
            return ans;
        }

        private static int[] Read(string input)
        {
            string[] inputs = input.Split(' ');
            int num = inputs.Length;
            int[] ints = new int[num];
            for (int i = 0; i < num; i++)
            {
                ints[i] = int.Parse(inputs[i]);
            }
            
            return ints;
        }


    }
}