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 find_max(a):
    n = len(a)

    if n <= 3:
        return max(a)

    dp = [[-(1 << 64)] * (2 + n % 2) for _ in range(n)]

    for i in range(2 + n % 2):
        dp[i][i] = a[i]
        dp[i + 1][i] = a[i]

    for i in range(2, n):
        for j in range(2 + n % 2):
            for extra_space in range(j + 1):
                curr_sum = dp[i - (2 + extra_space)][j - extra_space] + a[i]
                if curr_sum > dp[i][j]:
                    dp[i][j] = curr_sum

    return dp[-1][1 + n % 2]


def main():
    _ = int(input())
    a = list(map(int, input().split()))

    print(find_max(a))


main()
