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# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using static System.Math;
using static System.Array;
using static AtCoder.IO_ShortCut;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        //const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 };
        static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            int N = Int;
            var A = _ReadSplitLong;
            var dp = new long[N + 1, 3];
            if (N % 2 == 0)
            {
                long a = 0, b = 0;
                for(var i = 0; i < N; i++)
                {
                    if (i % 2 == 0) a += A[i];
                    else b += A[i];

                }
                OutL(Max(a, b));
                return;
            }
            for(var i = 0; i < N+1; i++)
            {
                for(var j = 0; j < 3; j++)
                {
                    dp[i, j] = -SINF;
                }
            }
            dp[0, 0] = 0;
            dp[0, 1] = dp[0, 2] = -SINF;

            for(var i = 0; i < N; i++)
            {
                for(var j = 0; j < 3; j++)
                {
                    if ((i + j) % 2 == 0)
                    {
                        dp[i + 1, j] = Max(dp[i + 1, j], dp[i, j] + A[i]);
                        if (j < 2) dp[i + 1, j + 1] = Max(dp[i + 1, j + 1], dp[i, j]);
                    }
                    else
                    {
                        dp[i + 1, j] = Max(dp[i + 1, j], dp[i, j]);
                        if (j < 2) dp[i + 1, j + 1] = Max(dp[i + 1, j + 1], dp[i, j]);
                    }
                }
            }
            OutL(dp[N, 2]);


            //Console.Out.Flush();
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }
        }
    }
    public class SegmentTree<T>
    {
        //
        //
        // 0-indexed!!!!!!!!!!!!!!!!!!!!!!!
        // [l,r)は半開区間!!!!!!!!!!!!!!!!!!!
        //
        int n;
        T[] Tree;
        Func<T, T, T> f;
        T ex;
        public SegmentTree(int size, Func<T, T, T> fun, T exvalue)
        {
            f = fun;
            ex = exvalue;
            n = 1;
            while (n < size) n <<= 1;
            Tree = new T[(n << 1) - 1];
            for (var i = 0; i < Tree.Length; i++) Tree[i] = ex;
        }
        public SegmentTree(int size, Func<T, T, T> f, T exvalue, T initial) : this(size, f, exvalue)
        {
            for (var i = 0; i < size; i++) Tree[i + n - 1] = initial;
            Set_All();
        }

        public void Set_All()
        {
            for (var i = n - 2; i >= 0; i--)
            {
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void Assign(int ind, T val)
        {
            Tree[ind + n - 1] = val;
        }
        public void Update(int ind)
        {
            int i = ind + n - 1;
            while (i > 0)
            {
                i = (i - 1) >> 1;
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void Query_Update(int ind, T val)
        {
            Assign(ind, val);
            Update(ind);
        }
        public T Query_Answer(int l, int r) //[l,r)
        {
            return Scanning(l, r, 0, 0, n);
        }
        private T Scanning(int l, int r, int ind, int ind_l, int ind_r)
        {
            if (ind_r <= l || r <= ind_l) { return ex; }
            if (l <= ind_l && ind_r <= r) { return Tree[ind]; }
            return f(Scanning(l, r, (ind << 1) + 1, ind_l, (ind_l + ind_r) >> 1), Scanning(l, r, (ind << 1) + 2, (ind_l + ind_r) >> 1, ind_r));
        }

        public T Look(int ind)
        {
            return Tree[ind + n - 1];
        }
        public void Debug_Display_All()
        {
            for (var i = 0; i < n; i++) Console.Write($"{Tree[i + n - 1]} ");
            Console.WriteLine();
        }
    }
    static class IO_ShortCut
    {
        public static string[] _ReadSplit => Console.ReadLine().Split();
        public static int[] _ReadSplitInt => ConvertAll(Console.ReadLine().Split(), int.Parse);
        public static long[] _ReadSplitLong => ConvertAll(Console.ReadLine().Split(), long.Parse);
        public static double[] _ReadSplit_Double => ConvertAll(Console.ReadLine().Split(), double.Parse);
        public static string Str => Console.ReadLine();
        public static int Int => int.Parse(Console.ReadLine());
        public static long Long => long.Parse(Console.ReadLine());
        public static double Double => double.Parse(Console.ReadLine());
        public static T Conv<T>(string input) => (T)Convert.ChangeType(input, typeof(T));
        public static void Input<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public static void Input<T, U>(out T a, out U b)
        { var q = _ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]); }
        public static void Input<T, U, V>(out T a, out U b, out V c)
        { var q = _ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]);c = Conv<V>(q[2]); }
        public static void Input<T, U, V, W>(out T a, out U b, out V c, out W d)
        { var q = _ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]);d = Conv<W>(q[3]); }

        public static void OutL(object s) => Console.WriteLine(s);
        public static void Out_Sep<T>(IEnumerable<T> s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_Sep<T>(IEnumerable<T> s, string sep) => Console.WriteLine(string.Join($"{sep}", s));
        public static void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_One(object s) => Console.Write($"{s} ");
        public static void Out_One(object s, string sep) => Console.Write($"{s}{sep}");
        public static void Endl() => Console.WriteLine();
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            array = ConvertAll(array, x => initialvalue);
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }
        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }
        static public long LPow(int a, int b) => (long)Pow(a, b);
        static public bool Bit(long x, int dig) => ((1L << dig) & x) != 0;
    }
    class Modulo
    {
        private int M;
        private readonly long[] m_facs;
        public long Mul(long a, long b)
        {
            return ((a * b) % M);
        }
        public Modulo(long n, int m)
        {
            M = m;
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public long Fac(long n)
        {
            return m_facs[n];
        }
        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1L;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public long Div(long a, long b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public long Ncr(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
    }
}