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.Generic;
class Program
    {
        static void Main(string[] args)
        {   
            int n = int.Parse(Console.ReadLine());
            string[] s = Console.ReadLine().Split(' ');
            int[] a = new int[n];
            for (int i=0; i<n; i++) a[i] = int.Parse(s[i]);
            int[] aPlus = new int[n];
            int minusCount = 0;
            int aPlusMin = 1000000000; 
            long aPlusSum = 0;
            for (int i=0; i<n; i++)
            {
                if (a[i] < 0)
                {
                    minusCount++;
                    aPlus[i] = -a[i];
                }
                else aPlus[i] = a[i];
                aPlusMin = Math.Min(aPlusMin, aPlus[i]);
                aPlusSum += (long)aPlus[i];
            }
            if (minusCount % 2 == 0) Console.WriteLine(aPlusSum);
            else Console.WriteLine(aPlusSum - aPlusMin * 2);
        }
    }
    //mcs Main.cs
    //mono Main.exe