Problem:
Score : 600 points

Problem Statement

Given is an integer sequence A_1, ..., A_N of length N.

We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from this sequence so that no two adjacent elements are chosen.

Find the maximum possible sum of the chosen elements.

Here \lfloor x \rfloor denotes the greatest integer not greater than x.

Constraints

2 \leq N \leq 2\times 10^5

|A_i|\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the maximum possible sum of the chosen elements.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49

Sample Output 4

295

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

namespace abc162
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var sStrList = Console.ReadLine().Split(' ');
            var sList = new List<long>();
            foreach (var sStr in sStrList)
            {
                sList.Add(long.Parse(sStr));
            }
            Console.WriteLine(GetMax(sList, sList.Count / 2));
        }

        private static long GetMax(List<long> list, int count)
        {
            //Console.WriteLine("List {0}, Count {1}", list.Count, count);
            if (count == 1)
            {
                var max = list[0];
                for (var i = 1; i < list.Count; ++i)
                {
                    if (max < list[i])
                    {
                        max = list[i];
                    }
                }
                return max;
            }
            if (list.Count % 2 == 0)
            {
                return GetMaxEven(list);
            }
            long left;
            long center;
            long right;
            long center2 = long.MinValue;
            if (list.Count / 2 + 1 == count)
            {
                return GetSkiped(list);
            }
            if (list.Count == 5)
            {
                left = list[0] + GetMax(list.GetRange(2, 3), 1);
                center = GetMax(list.GetRange(0, 2), 1) + GetMax(list.GetRange(3, 2), 1);
                right = GetMax(list.GetRange(0, 3), 1) + list[4];
            }
            else if (count % 2 == 0)
            {
                left = GetMax(list.GetRange(0, count - 2), count / 2 - 1) + list[count - 1]
                    + GetMax(list.GetRange(count + 1, count), count / 2);
                center = GetMax(list.GetRange(0, count - 1), count / 2 - 1) + list[count]
                    + GetMax(list.GetRange(count + 2, count - 1), count / 2);
                center2 = GetMax(list.GetRange(0, count - 1), count / 2) + list[count]
                    + GetMax(list.GetRange(count + 2, count - 1), count / 2 - 1);
                right = GetMax(list.GetRange(0, count), count / 2) + list[count + 1]
                    + GetMax(list.GetRange(count + 3, count - 2), count / 2 - 1);
            }
            else
            {
                left = GetMax(list.GetRange(0, count - 2), count / 2) + list[count - 1]
                    + GetMax(list.GetRange(count + 1, count), count / 2);
                center = GetMax(list.GetRange(0, count - 1), count / 2) + list[count]
                    + GetMax(list.GetRange(count + 2, count - 1), count / 2);
                right = GetMax(list.GetRange(0, count), count / 2) + list[count + 1]
                    + GetMax(list.GetRange(count + 3, count - 2), count / 2);
            }
            var res = left;
            if (res < center)
            {
                res = center;
            }
            if (res < center2)
            {
                res = center2;
            }
            if (res < right)
            {
                res = right;
            }
            return res;
        }
        private static long GetMaxEven(List<long> list)
        {
            //Console.WriteLine(" Even");
            var current = GetSkiped(list);
            var max = current;
            for (var i = list.Count - 2; i >= 0; i -= 2)
            {
                current = current - list[i] + list[i + 1];
                if (max < current)
                {
                    max = current;
                }
            }
            return max;
        }
        private static long GetSkiped(List<long> list)
        {
            var current = 0L;
            for (var i = 0; i < list.Count; i += 2)
            {
                current += list[i];
            }
            return current;
        }
    }
}