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

sys.setrecursionlimit(10 ** 6)

def find(idx, c, arr, tb):

    if c == 0:
        return 0

    if idx <= 0 or idx < 2 * c - 1:
        return float('-inf')

    if (idx, c) in tb:
        return tb[(idx, c)]

    rs = find(idx - 2, c - 1, arr, tb) + arr[idx - 1]
    rs = max(rs, find(idx - 1, c, arr, tb))

    tb[(idx, c)] = rs
    return rs

def main():

    n = int(input())
    arr = [int(e) for e in input().split(' ')]
    print(find(n, n // 2, arr, {}))
    return 0


main()
