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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(ReadLine());
        var A = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

        var sortedA = A.OrderBy(x => x).ToArray();

        var minusIndex = sortedA.LowerBound(0);

        if (minusIndex % 2 == 0)
        {
            for (int i = 0; i < minusIndex; i++)
                sortedA[i] *= -1;
        }
        else
        {
            if(minusIndex < N && Math.Abs(sortedA[minusIndex - 1]) > sortedA[minusIndex])
            {
                for (int i = 0; i < minusIndex + 1; i++)
                    sortedA[i] *= -1;
            }
            else
            {
                for (int i = 0; i < minusIndex - 1; i++)
                    sortedA[i] *= -1;
            }
        }

        var ans = sortedA.Sum(x => (long)x);

        WriteLine(ans);
    }
}
static class BinarySearchExtensions
{
    public static int LowerBound<T>(this List<T> list, T item, bool isDescending = false) where T : IComparable<T> =>
        ~list.BinarySearch(item, new LowerAndUpperBoundCompare<T>(true, isDescending));
    public static int UpperBound<T>(this List<T> list, T item, bool isDescending = false) where T : IComparable<T> =>
        ~list.BinarySearch(item, new LowerAndUpperBoundCompare<T>(false, isDescending));

    public static int LowerBound<T>(this T[] array, T item, bool isDescending = false) where T : IComparable<T> =>
        ~Array.BinarySearch(array, item, new LowerAndUpperBoundCompare<T>(true, isDescending));
    public static int UpperBound<T>(this T[] array, T item, bool isDescending = false) where T : IComparable<T> =>
        ~Array.BinarySearch(array, item, new LowerAndUpperBoundCompare<T>(false, isDescending));

    private class LowerAndUpperBoundCompare<T> : IComparer<T> where T : IComparable<T>
    {
        public LowerAndUpperBoundCompare(bool isLowerBound, bool isDescending) =>
            (this.isLowerBound, this.isDescending) = (isLowerBound, isDescending);

        private readonly bool isLowerBound, isDescending;

        public int Compare(T x, T y) => Predicate(x, y) ? 1 : -1;

        private bool Predicate(T x, T y)
        {
            var compareResult = x.CompareTo(y);
            return (isDescending ? (compareResult < 0) : (compareResult > 0)) || (isLowerBound && (compareResult == 0));
        }
    }
}