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: Accepted)

using System;
using System.Linq;
using System.Threading.Tasks;

static class Program
{
static void Main()
{
    int nGem = int.Parse(Console.ReadLine());
    var values = Console.ReadLine().Split(' ').Select(c => long.Parse(c));
  //int nGem = 5;
  //var values = new long[] { -1000000000,1000000000,-1000000000,1000000000,-1000000000,0,1000000000,-1000000000,1000000000,-1000000000,1000000000};
  bool isEven = (values.Select(v => v < 0 ? 1 : 0).Sum() % 2 == 0);
  isEven |= values.Any(v => v == 0);
  var absValue = values.Select(v => Math.Abs(v));
  long result =   absValue.Sum();
  if(isEven == false)
  {
    long adjust = absValue.Min() * 2;
    result -= adjust;
  }
  Console.WriteLine(result);
}
}