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
import sys
input = sys.stdin.readline


if __name__ == '__main__':

    N = int(input())
    A = list(map(int, input().split()))

    dp = [0] * N
    dp[1] = max(A[0], A[1])
    c = A[0]

    for i in range(2, N):
        if i % 2 == 0:
            dp[i] = max(dp[i - 2] + A[i], dp[i - 1])
            c += A[i]
        else:
            dp[i] = max(dp[i - 2] + A[i], c)

    print(dp[-1])
