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 proconio::{fastout, input};
use std::cmp::max;

const MIN: i64 = -0x7fffffffffffffff;

#[fastout]
fn main() {
    input! {in_n: usize, in_a: [i64; in_n]};
    let mut dp = Vec::new();

    for _ in 0..(in_n % 2 + 2) {
        dp.push(vec![MIN; in_n / 2]);
    }

    for i in 0..dp.len() {
        dp[i][0] = in_a[i];
    }

    for i in 1..(in_n / 2) {
        let p = i * 2;

        for j in 0..dp.len() {
            for k in 0..=j {
                dp[j][i] = max(dp[k][i - 1] + in_a[p + j], dp[j][i]);
            }
        }
    }

    let mut maxval = MIN;

    for i in 0..dp.len() {
        maxval = max(dp[i][dp[i].len() - 1], maxval);
    }

    println!("{}", maxval);
}