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)

use proconio::{fastout, input};

use std::cmp::max;

#[fastout]
fn main() {
    input! {
        n: usize,
        aa: [i64; n]
    }
    let mut u = vec![0; n + 1];
    let mut v = vec![0; n + 1];
    let mut w = vec![0; n + 1];
    let mut x = vec![0; n + 1];
    let mut y = vec![0; n + 1];
    let mut z = vec![0; n + 1];
    for i in 0..n {
        u[i + 1] = x[i] + aa[i];
        v[i + 1] = y[i] + aa[i];
        w[i + 1] = z[i] + aa[i];
        x[i + 1] = u[i];
        y[i + 1] = max(x[i], v[i]);
        z[i + 1] = max(y[i], w[i]);
    }
    // println!("{} {} {} {} {} {}", u[n], v[n], w[n], x[n], y[n], z[n]);
    // println!("{}", max(w[n], y[n]));
    println!("{}", max(v[n], max(w[n], max(x[n], y[n]))));
}