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.Collections.Generic;
using System.Linq;
using System.Text;

public class AtCoderF
{
    static void Main()
    {
        var sc = new Scanner();

        int n = sc.NextInt();
        long[] a = sc.LongArray();

        long[] memo = new long[n];
        long[] evenSum = new long[n];

        evenSum[0] = a[0];
        for (int i = 2; i < n; i += 2)
        {
            evenSum[i] = evenSum[i - 2] + a[i];
        }

        memo[0] = 0;
        memo[1] = Math.Max(a[0], a[1]);
        for (int i = 2; i < n; i++)
        {
            long tmpAnswer = 0;

            // 自分を選んだ場合
            long answer1 = a[i] + memo[i - 2];

            // 自分の1つ前を選んだ場合
            long answer2 = a[i - 1] + (i >= 3 ? memo[i - 3] : 0);

            tmpAnswer = Math.Max(answer1, answer2);

            if (i % 2 == 0)
            {
                // 自分、自分の1つ前、のどちらも選ばない場合
                long answer3 = evenSum[i - 2];

                tmpAnswer = Math.Max(tmpAnswer, answer3);
            }

            memo[i] = tmpAnswer;
        }

        long answer = memo[n - 1];

        Console.WriteLine(answer);
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}