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()))
if N%2:
    a=[None]*N
    b=[None]*N
    c=[None]*N
    a[0]=A[0]
    b[1]=A[1]
    c[2]=A[2]
    for i in range(2,N-2,2):
        a[i]=a[i-2]+A[i]
    for i in range(3,N,2):
        b[i]=max(a[i-3],b[i-2])+A[i]
    for i in range(4,N,2):
        c[i]=max(a[i-4],b[i-3],c[i-2])+A[i]
    print(max(a[-3],b[-2],c[-1]))
else:
    a=[None]*N
    b=[None]*N
    a[0]=A[0]
    for i in range(2,N,2):
        a[i]=a[i-2]+A[i]
    b[1]=A[1]
    for i in range(3,N,2):
        b[i]=max(a[i-3],b[i-2])+A[i]
    print(max(a[-2],b[-1]))