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;
using System.Collections.Generic;

namespace ABC125 {
  class ProblemD {
    static void Main(string[] args) {
      int n = Input.num;
      long[] a = Input.numLs;

      int cnt = 0;
      long sum = 0, min = 0;
      for (int i = 0; i < n; i++) {
        if (a[i] < 0) {
          cnt++;
          a[i] *= -1;
        }
      }
      
      if (cnt % 2 == 0) { // even
        for (int i = 0; i < n; i++) {
          sum += a[i];
        }
      } else {  // odd
        min = Min(a);
        for (int i = 0; i < n; i++) {
          if (a[i] != min) {
            sum += a[i];
          } else {
            sum -= a[i];
          }
        }
      }
      System.Console.WriteLine(sum);
    }
    public static long Min(long[] array) {
      long ret = array[array.Length - 1];
      for (int i = 0; i < array.Length - 1; i++) {
        if (ret > array[i]) {
          ret = array[i];
        }
      }
      return ret;
    }
  }
  public class Input {
    public static string str => System.Console.ReadLine();
    public static string[] strs => str.Split(' ');
    public static char[] charArr => str.ToCharArray();
    public static int num => int.Parse(str);
    public static int[] nums => Array.ConvertAll(strs, int.Parse);
    public static long numL => long.Parse(str);
    public static long[] numLs => Array.ConvertAll(strs, long.Parse);
  }
}