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=int(input())
a=[int(i) for i in input().split()]
INF=float('inf')
dp0=defaultdict(lambda: -INF)
dp1=defaultdict(lambda: -INF)
dp0[(0,0)]=0
for i in range(1,n+1):
  for j in range(i//2-1,(i+1)//2+1):
    dp0[(i,j)]=max(dp0[(i-1,j)],dp1[(i-1,j)])
    dp1[(i,j)]=dp0[(i-1,j-1)]+a[i-1]
print(max(dp0[(n,n//2)],dp1[(n,n//2)]))