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
N=int(input())
A=list(map(int,input().split()))
from collections import deque
q=deque([(-1,0,-2,0)])
ans=-10**18
for i,a in enumerate(A):
    d={}
    while q and q[0][0]<i:
        j,n,r,x=q.popleft()
        if r<-1:
            if n==N//2-1:
                ans=max(ans,x+a)
            elif n not in d:
                d[n]=x
            elif d[n]<x:
                d[n]=x
        if (j+1)//2<=n:
            q.append((i,n,r-1,x))
    for n,x in d.items():
        q.append((i,n+1,-1,x+a))
print(ans)