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: Accepted)

use std::cmp::max;
use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
}

macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, n: usize);
    parse!(it, a: [i64; n]);
    let mut memo = vec![vec![0, 0]; n];
    fn get(memo: &mut Vec<Vec<i64>>, i: usize, n: usize, pat: usize, a: &Vec<i64>) -> i64 {
        if memo[i][pat] != 0 {
            return memo[i][pat];
        }
        match (n - i, pat) {
            (2, 0) => return max(a[i], a[i + 1]),
            (3, 0) => return max(a[i], max(a[i + 1], a[i + 2])),
            (3, 1) => return a[i] + a[i + 2],
            (4, 0) => return max(get(memo, i + 2, n, 0, a) + a[i], a[i + 1] + a[i + 3]),
            _ => (),
        }
        if (n - i) % 2 == 1 {
            if pat == 1 {
                let ret = get(memo, i + 2, n, 1, a) + a[i];
                memo[i][pat] = ret;
                ret
            } else {
                let ret = max(
                    get(memo, i + 2, n, 0, a) + a[i],
                    get(memo, i + 3, n, 0, a) + a[i + 1],
                );
                let ret = max(ret, get(memo, i + 2, n, 1, a));
                memo[i][pat] = ret;
                ret
            }
        } else {
            let ret = max(
                get(memo, i + 2, n, 0, a) + a[i],
                get(memo, i + 3, n, 1, a) + a[i + 1],
            );
            memo[i][pat] = ret;
            ret
        }
    }
    println!("{}", get(&mut memo, 0, n, 0, &a));
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}