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 ConsoleApp1
{
	class Program5
	{

		static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());
			var an = Console.ReadLine().Split(' ');
			List<int> alist = new List<int>();
			for (int i = 0; i < n; i++)
			{
				alist.Add(int.Parse(an[i]));
			}

			bool b = true;
			while (b)
			{
				b = false;
				for (int i = 0; i < n; i++)
				{
					if (alist[i] < 0)
					{
						int l = 0;
						int r = 0;
						if (i != 0)
						{
							l = (-alist[i] + -alist[i - 1]) - (alist[i] + alist[i - 1]);
						}

						if (i != n - 1)
						{
							r = (-alist[i] + -alist[i + 1]) - (alist[i] + alist[i + 1]);
						}

						if (l > r && l > 0)
						{
							b = true;
							alist[i] = -alist[i];
							alist[i - 1] = -alist[i - 1];
						}
						if (r > l && r > 0)
						{
							b = true;
							alist[i] = -alist[i];
							alist[i + 1] = -alist[i + 1];
						}
					}
				}
			}

			int max = 0;
			for (int i = 0; i < n; i++)
			{
				max += alist[i];
			}

			Console.Write(max.ToString() + "\n");
//			Console.ReadLine();
		}
	}
}