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