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.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var A = cin.ReadLongArray(N);
			long Res = A.Sum(a => Abs(a));
			var hasZero = Enumerable.Range(0, N).Any(i => A[i]==0);
			if(!hasZero) {
				var negas = A.Count(a => a<0);
				if(negas%2!=0)
					Res-=2*A.Select(a => Abs(a)).Min();
			}
			Console.WriteLine(Res);
		}
	}
	static class ExtendClass {
		public static void Swap<T>(this T[] A, int x, int y) {
			var tmp = A[x];
			A[x]=A[y];
			A[y]=tmp;
		}
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
		public static IEnumerable<int> Indices<T>(this T[] X) => Enumerable.Range(0, X.Length);
		public static IEnumerable<int> Indices<T>(this T[,] X, int dim)
			=> Enumerable.Range(0, X.GetLength(dim));
		public static string Join<T>(this T[,] X, string separatorD2 = ",", string separatorD1 = "\n")
			=> X.Indices(0).Select(
				i => X.Indices(1).Select(j => X[i, j]).Join(separatorD2)
			).Join(separatorD1);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}

}