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
def main():
    import sys
    input=sys.stdin.readline
    n=int(input())
    A=list(map(int,input().split()))
    A_=[0]*n
    for i in range(n):
        if i%2==0:
            A_[i]=A[i]
        else:
            A_[i]==0
    for i in range(n-1):
        A_[i+1]+=A_[i]
    dp=[0]*n
    dp[1]=max(A[0],A[1])
    for i in range(2,n):
        if i%2==0:
            dp[i]=max(dp[i-2]+A[i],dp[i-1])
        else:
            dp[i]=max(dp[i-2]+A[i],A_[i-1])
    print(dp[n-1])
if __name__ == '__main__':
    main()