P8681 [AtCoder] AtCoder Beginner Contest 162 - Select Half
提高-
题目描述

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.

Examples

Input

6
1 2 3 4 5 6

Output

12

Input

5
-1000 -100 -10 0 10

Output

0

Input

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output

5000000000

Input

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

Output

295

输入格式

见题面

输出格式

见题面

样例输入
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
样例输出
295