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.Collections.Generic;
using static program.Input;
using static program.MyMath;
using static System.Console;

namespace program {
  class Program {
    static string Alp = "abcdefghijklmnopqrstuvwxyz";
    static void Main()
    {
      var n = ScanInt();
      var a = ScanLongArray();
      var c = a.Count(_=>_<=0);
      a = a.Select(_=>Math.Abs(_)).ToArray();
      long res = a.Sum() - (c%2==1 ? 2*a.Min() : 0);
      WriteLine(res);
    }
  }
  
  static class Input {
    static public int ScanInt() { return int.Parse(Console.ReadLine()); }
    static public uint ScanUint() { return uint.Parse(Console.ReadLine()); }
    static public double ScanDouble() { return double.Parse(Console.ReadLine()); }
    static public long ScanLong() { return long.Parse(Console.ReadLine()); }
    static public ulong ScanUlong() { return ulong.Parse(Console.ReadLine()); }
    static public int[] ScanIntArray() { return Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray(); }
    static public uint[] ScanUintArray() { return Console.ReadLine().Split().Select(x => uint.Parse(x)).ToArray(); }
    static public double[] ScanDoubleArray() { return Console.ReadLine().Split().Select(x => double.Parse(x)).ToArray(); }
    static public long[] ScanLongArray() { return Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray(); }
    static public ulong[] ScanUlongArray() { return Console.ReadLine().Split().Select(x => ulong.Parse(x)).ToArray(); }

    static public string ScanStr() { return Console.ReadLine(); }
    static public string[] ScanStrArray() { return ScanStr().Split(); }
  }
  
  static class MyMath {
    public static int GCD(int a, int b) {
        Func<int, int, int> gcd = null;
        gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
        return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static long GCD(long a, long b) {
        Func<long, long, long> gcd = null;
        gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
        return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static ulong extGCD(ulong a, ulong b, ref ulong x, ref ulong y) {
      if(b==0) {
        x=1; 
        y=0;
        return a;
      }
      var d = extGCD(b, a%b, ref y, ref x);
      y -= a/b *x;
      return d;
    }
    public static int LCM(int a, int b) { return a * b / GCD(a, b); }
    public static long LCM(long a, long b) { return a * b / GCD(a, b); }
  }
}