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.Linq;
using System.IO;
using System.Collections.Generic;
using static System.Math;

class P
{
  static int[] Input(){
    return Console.ReadLine().Split().Select(int.Parse).ToArray();
  }
  static void Main()
  {
    int[] NK = Input();
    int N = NK[0];
    int[] A = Input();
    long R = 0;
    int mnx = 1000000000;
    for(int i=0;i<N-1;i++){
      if (A[i]<0){
        A[i] *= -1;
        A[i+1] *= -1;
      }
      R += A[i];
      mnx = Min(A[i], mnx);
    }
    var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
    Console.SetOut(sw);
    if (A[N-1]<0){
      mnx = Min(A[N-1]*(-1), mnx);
      Console.WriteLine(R-A[N-1] - 2*mnx);
    }else{
      Console.WriteLine(R+A[N-1]);
    }
    Console.Out.Flush();
  }
}