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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define FasterIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
typedef unsigned long long ull;
typedef long long ll;
typedef double db;

#define mem(a,x) memset(a,x,sizeof(a))
#define pb push_back
#define ff first
#define ss second
#define mk make_pair
#define pi pair<int,int>
#define vi vector<int>
#define pL pair<ll,ll>
#define vL vector<ll>
#define vp vector<pi>
#define vpL vector<pL>

const int MX=1000000;
const ll inf=1e9;
const ll mod=998244353;


int R[MX];
ll dp[MX];

int main()
{
    FasterIO;

    int n;ll sm1=0;
    cin>>n;
    for(int i=1; i<=n; sm1+=R[i], i++) cin>>R[i];

    for(int i=n; i>=1; i--) dp[i]=R[i]+max(dp[i+2], dp[i+3]);

    if(n&1) cout<<max({dp[1], dp[2], dp[3]})<<endl;
    else    cout<<max(dp[1], dp[2])<<endl;
    return 0;
}