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;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var seqA = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

        var suffix = 0L;
        for (int i = 1 + n % 2; i < seqA.Length; i += 2)
        {
            suffix += seqA[i];
        }

        var max = suffix;
        var ps = new long[2];
        for (int i = 2; i < seqA.Length; i += 2)
        {
            var window = seqA.AsSpan(i - 2, 3);
            suffix -= window[2];
            ps[0] = ps.Max() + window[1];
            ps[1] += window[0];
            max = Math.Max(max, ps.Max() + suffix);
        }

        Console.WriteLine(max);
    }
}