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: Wrong Answer)

using System;
namespace ForATCODER
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int N = s2i(Console.ReadLine());
            int[] an = S2Iarray(Console.ReadLine().Split(' '));
            int n2 = (int)Math.Floor(N / 2.0f);
            int[] indices = new int[an.Length];
            for (int i = 0; i < indices.Length; i++) indices[i] = i;
            Array.Sort(an, indices);
            ulong sum = 0;
            for (int i = an.Length-1;i >=0;i-=2)
            {
                sum += (ulong)an[i];
            }
            Console.WriteLine(sum);

        }
  

        static int s2i(String s)
        {
            return Convert.ToInt32(s);
        }
        static void RESULT(int res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(String res)
        {
            Console.WriteLine(res);
        }
        static String[] ReadLineAll(int count)
        {
            String[] res = new String[count];
            for (int i = 0; i < count; i++)
            {
                res[i] = Console.ReadLine();
            }
            return res;
        }

        static int[] S2Iarray(String[] src)
        {
            int len = src.Length;
            int[] res = new int[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt32(src[i]);
            }
            return res;
        }
    }
}