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::input;
use std::cmp;

fn main() {
  input! {
    n: usize,
    mut a: [i64; n],
  }

  let INF_LL: i64 = 1_000_000_000_000_000_000;
  let mut dp: [[i64; 2]; 5] = [[-INF_LL; 2]; 5];
  dp[2][0] = 0;
  // dp[i][j] := select - not is i and (selected i-1 if j == 1))

  for x in a {
    let mut dp2: [[i64; 2]; 5] = [[-INF_LL; 2]; 5];
    for j in 0..5 as usize {
      for k in 0..2 as usize {
        if j > 0 {
          dp2[j - 1][0] = std::cmp::max(dp2[j - 1][0], dp[j][k]);
        }
        if j < 4 && k == 0 {
          dp2[j + 1][1] = std::cmp::max(dp2[j + 1][1], dp[j][k] + x);
        }
      }
    }
    dp = dp2;
  }
  let sa: i32 = n as i32 /2 - (n as i32  - n as i32/2);
  println!("{}", std::cmp::max(dp[(sa+2) as usize][0], dp[(sa+2) as usize][1]));
}