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 functools
import sys

sys.setrecursionlimit(1000000)

N, = (int(x) for x in input().split())
arr = [int(x) for x in input().split()]

@functools.lru_cache(None)
def dp(i, k):
    if k <= 0:
        return 0
    rem = N - i
    if k > (rem // 2) + (rem % 2):
        return -float('inf')
    return max(arr[i] + dp(i + 2, k - 1), dp(i + 1, k))


sol = dp(0, N // 2)

print(sol)
