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;

void file() {
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
}

void fast()
{
    std::ios_base::sync_with_stdio(0);
    cin.tie(NULL); cout.tie(NULL);
}

const int MX = 2e5 + 5;

long long n, arr[MX], dp[MX][3];

void read()
{
    cin>>n;
    for (int i = 0; i < n; ++i)
    {
        cin>>arr[i];
    }
}

long long solve(long long idx, long long rem)
{
    if (idx >= n)
    {
        return rem == 2 ? LLONG_MIN : 0;
    }
    long long &ret = dp[idx][rem];

    if (~ret)
    {
        return ret;
    }
    ret = LLONG_MIN;
    ret = max(ret, solve(idx + 2, rem) + arr[idx]);
    if (rem)
    {
        ret = max(ret, solve(idx + 1, rem - 1));
    }
    return ret;

}
int main(int argc, char const *argv[])
{
    file();
    
    read();

    memset(dp, -1, sizeof(dp));
    
    cout<<solve(0, (n & 1) + 1);




}