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-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Solve{
    static public int mod = 1000000007;
    public static void Main(){
        // 方針
        // 実装が地味にやりづらい
        var n = rint();
        var sel = n/2;
        var list = inta();
        if(n==2){
            WriteLine(Max(list[0],list[1]));
        }else if(n==3){
            long max = Max(list[0],list[1]);
            max = Max(max,list[2]);
            WriteLine(max);
        }else if(n%2==0){
            var l = new long[sel];
            var r = new long[sel];
            for(int i=0;i<sel;i++){
                l[i] = list[i*2];
                if(i>0) l[i] += l[i-1];
            }
            Array.Reverse(list);
            for(int i=0;i<sel;i++){
                r[i] = list[i*2];
                if(i>0) r[i] += r[i-1];
            }
            Array.Reverse(r);
            Array.Reverse(list);
            long max = 0;
            for(int i=0;i<=sel;i++){
                if(i==0){
                    max = r[0];
                }else if(i== sel){
                    max = Max(max,l[i-1]);
                }else{
                    max = Max(r[i]+l[i-1],max);
                }
            }
            WriteLine(max);
        }else{
            var l = new long[n];
            var r = new long[n];
            for(int i=0;i<n;i++){
                if(i%2 == 0) l[i] = list[i];
            }
            for(int i=1;i<n;i++){
                l[i] += l[i-1];
            }
            Array.Reverse(list);
            for(int i=0;i<n;i++){
                if(i%2 == 0) r[i] = list[i];
            }
            for(int i=1;i<n;i++){
                r[i] += r[i-1];
            }
            Array.Reverse(r);
            long max = 0;
            Array.Reverse(list);
            for(int i=0;i<sel;i++){
                int lno = i*2;
                long tempm = Max(list[lno],list[lno+1]);
                tempm = Max(list[lno+2],tempm);
                if(i == 0){
                    max = r[lno+4] + tempm;
                    //WriteLine($"{r[lno+4]} {max}");
                }else if(i==sel-1){
                    max = Max(l[lno-2] + tempm,max);
                    //WriteLine($"{tempm} {l[lno-2]} {max}");
                }else{
                    max = Max(max,l[lno-2]+r[lno+4]+tempm);
                    //WriteLine($"{l[lno-2]} {r[lno+4]} {max}");
                }
                //WriteLine(max);
            }
            long wa = 0;
            for(int i=0;i<n;i++){
                if(i%2 == 1) wa += list[i];
            }
            long twa = Max(wa,wa-list[1]+list[0]);
            long ttwa = Max(wa,wa-list[n-2]+list[n-1]);
            wa = Max(wa,twa);
            wa = Max(wa,ttwa);
            
            WriteLine(Max(wa,max));
        }
        
        
        
        
        
        
    }
    // 1からaまでの数字並べ替え全通り返すやつ
    static List<string> permutation(int a){var list = new List<string>();if(a == 1){list.Add("1");return list;}else{foreach(var k in permutation(a-1)){var ch = k.ToCharArray();for(int i=0;i<=ch.Length;i++){string intemp = "";if(i == 0){intemp += a.ToString();}for(int j=0;j<ch.Length;j++){intemp += ch[j].ToString();if(i == j+1){intemp += a.ToString();}}list.Add(intemp);}}}return list;}
    public static void swap(ref int a,ref int b){int temp = a;a= b;b = temp;}
    static void charswap(ref char a,ref char b){char temp = a;a= b;b = temp;}
    static int ncr(int n,int r){r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    static int square2(int a,int b){long output = 1;var list = new List<long>();int sh = 1;long n = a;list.Add(a);while(sh < b){sh *= 2;n = n*n%mod;list.Add(n);}for(int i=list.Count-1;i>=0;i--){if(b > sh){b -= sh;sh /= 2;output = output*list[i]%mod;}}return (int)output;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static char[] chara(){ string[] a=stra();string b="";for(int i=0;i<a.Length;i++){b+=a[i];}return b.ToCharArray();}
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
}