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;
class Program
{
    static void Main(string[] args)
    {
            // 準備
            List<ClsInp> lstInp = new List<ClsInp>();

            // 入力
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            sS = System.Console.ReadLine().Trim().Split(' ');

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            int iMins = 0;      // マイナスの数
            int iZero = 0;      // 0の数
            for (int i = 0; i < sS.Length; i++)
            {
                ClsInp oneUsr = new ClsInp();
                oneUsr.iX = int.Parse(sS[i]);                           // 値
                oneUsr.iA = Math.Abs(oneUsr.iX);                        // 絶対値
                lstInp.Add(oneUsr);
                if (oneUsr.iX == 0) { iZero += 1; }                     // 0の数
                else if (oneUsr.iX != oneUsr.iA) { iMins += 1; }        // マイナスの数
            }
            long iOut = 0;
            if (iMins == 0) { iOut = lstInp.Sum(x => x.iA); }           // マイナスの数がない                →全部プラス
            else if (iMins % 2 == 0) { iOut = lstInp.Sum(x => x.iA); }  // マイナスの数が偶数                →全部プラス
            else if (iZero > 0) { iOut = lstInp.Sum(x => x.iA); }       // マイナスの数が奇数&0が1個でもある →全部プラス
            else                                                        // マイナスの数が奇数&0が1個もない   →絶対値の最小の1つだけマイナス
            {
                lstInp.Sort(delegate (ClsInp mca1, ClsInp mca2) { return (int)(mca1.iA - mca2.iA); });        // 絶対値の昇順
                iOut = lstInp.Sum(x => x.iA);                           // とりあえず全部プラス
                iOut -= lstInp[0].iA * 2;                               // そこから最小の1個だけマイナスとして考慮
            }

            // 出力
            System.Console.WriteLine("{0}", iOut.ToString());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

        private class ClsInp
        {
            public long iX { get; set; } = 0;    // 値
            public long iA { get; set; } = 0;    // 絶対値
        }

}