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
from collections import defaultdict
N,*A = map(int, open(0).read().split())
dic1 = defaultdict(lambda :-10**20)
dic2 = defaultdict(lambda :-10**20)
for i in range(-1,N):
  dic1[(i,0)] = 0
  dic2[(i,0)] = 0
for i in range(N):
  for j in range(max(1,N//2-(N-i+1)//2), i//2+2):
    dic1[(i,j)] = max(dic1[(i,j)],dic2[(i-1,j-1)]+A[i])
  for j in range(N//2-(N-i)//2,(i-1)//2+2):
    dic2[(i,j)] = max(dic2[(i-1,j)],dic1[(i-1,j)])
print(max(dic1[(N-1,N//2)],dic2[(N-1,N//2)]))