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;

class Program{
  static void Main(){
    int N = int.Parse(Console.ReadLine());
    long[] A = Console.ReadLine().Split(' ')
      .Select(x => long.Parse(x))
      .ToArray();
    
    int c_negative = 0; // 負の数の個数
    long min_abs = long.MaxValue; // 最も絶対値が小さい数（の絶対値）
    long sum = 0; //総和
    for (int i = 0; i < N; i++){
      min_abs = Math.Min(min_abs, Math.Abs(A[i]));
      sum += Math.Abs(A[i]);
      if (A[i] < 0)
        c_negative++;
    }
    
    if (c_negative % 2 == 1)
      sum -= min_abs * 2;
    Console.WriteLine(sum);
    
  }
}