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;
using System.Text;
using System.Threading.Tasks;

namespace ABC125C
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            var numbers = Console.ReadLine().Split().Select(long.Parse).ToList();
            var count = 0;
            var zerocount = 0;
            long sum = 0;
            long small = 0;
            var firstflag = true;
            long abs = 0;
            foreach (var number in numbers)
            {
                if (number == 0)
                {
                    zerocount++;
                    continue;
                }
                abs = Math.Abs(number);
                if (firstflag)
                {
                    small = number;
                    firstflag = false;
                }
                else
                {
                    if (small > abs)
                    {
                        small = abs;
                    }
                }
                sum += abs;
                if (number < 0)
                {
                    count++;
                }
            }
            if (count % 2 == 0 || zerocount >= count)
            {
                Console.WriteLine(sum);
            }
            else
            {
                Console.WriteLine(sum - small * 2);
            }
        }
    }
}