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.