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;

namespace ABC125D
{
    class MainClass
    {

        static long[] a;
        static int[] n;

        public static void Main(string[] args)
        {
            int INF = int.MinValue;
            n = Array.ConvertAll(Console.ReadLine().Split().ToArray(), int.Parse);
            a = Array.ConvertAll(Console.ReadLine().Split().ToArray(), long.Parse);

            long[,] dp = new long[n[0]+1, 2];
            dp[0, 0] = 0;
            dp[0, 1] = INF;
            for (int i = 0; i < n[0]; i++)
            {
                dp[i + 1, 0] = Math.Max(dp[i, 0] + a[i ], dp[i, 1] - a[i ]);
                dp[i + 1, 1] = Math.Max(dp[i, 0] - a[i ], dp[i, 1] + a[i ]);
            }
            Console.WriteLine(dp[n[0], 0]);

        }
    }
}