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.Collections;
using System.Collections.Generic;
using System.Linq;

public class Class1
{
	static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());

        string[] input = Console.ReadLine().Split(' ');
        long[] a = new long[N];
        for(int i = 0;i < N;i++)
        {
            a[i] = int.Parse(input[i]);
        }

        long[] b = new long[N];
        long absmin = 1000000;
        long absminAdd = 0;
        for(int i = 0;i < N;i++)
        {
            b[i] = Math.Abs(a[i]);
            if (b[i] < absmin)
            {
                absmin = b[i];
                absminAdd = i;
            }
        }

        long result = b.Sum() - b[absminAdd];

        //-count
        int upc = 0;
        int downc = 0;
        for(int i = 0;i < absminAdd;i++)
        {
            if (a[i] < 0) upc++;
        }

        for(int i = N - 1;i > absminAdd;i--)
        {
            if (a[i] < 0) downc++;
        }

        if (upc % 2 == 0 && downc % 2 == 0) result += a[absminAdd];
        else if (upc % 2 == 1 && downc % 2 == 1) result += a[absminAdd];
        else result += -1 * a[absminAdd];

        Console.WriteLine(result);
    }
}