Select Half

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 ... A_N

outputFormat

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

样例

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

295