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;
using System.Linq;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var N = int.Parse(ReadLine());
        var A = ReadLine().Split().Select(int.Parse).ToArray();

        var s = 0L;
        var c = 0;
        for (int i = 0; i < N; i++)
        {
            if (A[i] < 0) c++;
            s += Abs(A[i]);
        }
        if (c % 2 == 0)
        {
            WriteLine(s);
            return;
        }
        else
        {
            WriteLine(s-A.Select(x=>Abs(x)).Min()*2);
        }
    }
}

public class SegmentTree<T> where T : struct
{
    T[] buffer;
    int N;
    T IE;
    Func<T, T, T> Op;


    public SegmentTree(T[] init, T E, Func<T, T, T> op)
    {
        var c = 1;
        while (c < init.Length) c <<= 1;
        N = c;
        buffer = new T[N * 2 - 1];
        for (int i = 0; i < buffer.Length; i++)
        {
            buffer[i] = E;
        }
        Array.Copy(init, 0, buffer, N - 1, init.Length);
        for (int i = N - 2; i >= 0; i--)
        {
            buffer[i] = op(buffer[i * 2 + 1], buffer[i * 2 + 2]);
        }
        Op = op;
        IE = E;
    }

    public void Update(int index, T value)
    {
        index += N - 1;
        buffer[index] = value;
        while (index > 0)
        {
            index = (index - 1) / 2;
            buffer[index] = Op(buffer[index * 2 + 1], buffer[index * 2 + 2]);
        }
    }

    public T this[int index]
    {
        set
        {
            Update(index, value);
        }
        get
        {
            return buffer[index + N - 1];
        }
    }

    public T Query(int l, int r)
    {
        var y = IE;
        l += N - 1;
        r += N - 1;
        while (l < r)
        {
            if ((l & 1) == 0)
            {
                y = Op(y, buffer[l]);
            }
            if ((r & 1) == 0)
            {
                y = Op(y, buffer[r - 1]);
            }
            l /= 2;
            r = (r - 1) / 2;
        }
        return y;
    }
}