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 Rust (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
#![allow(unused_macros)]
#![allow(dead_code)]
use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{self, stdin, BufRead};
use std::str::FromStr;

fn read_one<T>() -> T
where
    T: FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    let stdin = stdin();
    let mut handle = stdin.lock();
    let mut buf = String::new();
    handle.read_line(&mut buf).unwrap();

    buf.trim().parse::<T>().unwrap()
}

macro_rules! read_tuple {
        ( $( $t:ty ), * ) => {
            {
                let stdin = stdin();
                let mut handle = stdin.lock();
                let mut buf = String::new();
                handle.read_line(&mut buf).unwrap();
                let mut v = buf.trim().split_whitespace()
                    .collect::<VecDeque<&str>>();
                (
                    $({
                        v.pop_front().unwrap().parse::<$t>().unwrap()
                    },)*
                )
            }
        }
    }

fn read_vec<T>() -> Vec<T>
where
    T: FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    let stdin = stdin();
    let mut handle = stdin.lock();
    let mut buf = String::new();
    handle.read_line(&mut buf).unwrap();

    buf.trim()
        .split_whitespace()
        .map(|s| s.parse::<T>().unwrap())
        .collect::<Vec<T>>()
}

fn rec(v: &[i64]) -> i64 {
    let mut sum1 = 0;
    let mut sum2 = 0;
    if v.len() == 0 {
        return 0;
    } else if v.len() % 2 == 0 {
        for i in 0..v.len() {
            if i % 2 == 0 {
                sum1 += v[i];
            } else {
                sum2 += v[i];
            }
        }
    } else {
        // don't select first
        if v.len() == 1 {
            return v[0];
        } else {
            sum1 = rec(&v[1..]);
            sum2 = v[0] + rec(&v[2..]);
        }
    }
    std::cmp::max(sum1, sum2)
}

fn main() -> io::Result<()> {
    let _ = read_one::<usize>();
    let v: Vec<i64> = read_vec();
    let ans = rec(&v[..]);
    println!("{}", ans);
    return Ok(());
}