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.

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.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $|A_i|\leq 10^9$
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分