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;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			var inputArray = retreiveLongArray();
			var inputCount = 1;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long N = inputArray[0];
			var AArray = retreiveLongArray();

			var minusCount = 0;
			var haveZero = false;

			for (int i = 0; i < N; i++) {
				if (AArray[i]==0) {
					haveZero = true;
				}
				if (AArray[i] <0) {
					minusCount++;
				}
			}

			//0がある場合
			if (haveZero) {
				var ans = AArray.Select(x =>Math.Abs(x)).Sum();
				Console.WriteLine(ans);
				return;
			}

			if (minusCount%2==0) {//マイナスの数偶数の場合、すべて正にできる
				var ans = AArray.Select(x => Math.Abs(x)).Sum();
				Console.WriteLine(ans);
				return;
			}

			var absArray = AArray.Select(x => Math.Abs(x));
			var min = absArray.Min();

			var ans2 = absArray.Sum() - min*2;
			Console.WriteLine(ans2);
		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}