101625: [AtCoder]ABC162 F - Select Half

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