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():
    from collections import defaultdict

    inf = 10 ** 15

    N = int(input())
    *a, = map(int, input().split())

    it = iter(a)

    dp = [defaultdict(lambda: -inf) for _ in range(N + 1)]
    dp[0][0] = 0
    dp[1][0] = 0
    dp[1][1] = next(it)
    for i, x in enumerate(it, 2):
        mi = (i - 1) // 2
        ma = (i + 1) // 2
        for taken_count in range(mi, ma + 1):
            dp[i][taken_count] = max(
                dp[i - 1][taken_count],
                dp[i - 2][taken_count - 1] + x
            )

    ans = dp[N][N // 2]

    print(ans)


if __name__ == '__main__':
    main()
