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 math
import sys
sys.setrecursionlimit(1000000)

N = int(input())
A = [int(i) for i in input().split()]

memo = {}
def sub_max(n, m):
    if((n, m) in memo):
        return memo[(n, m)]
    
    if(m == 1 and n >= 1):
        memo[(n, m)] = max(A[-n:])
        return memo[(n, m)]

    if(m > math.ceil(n/2)):
        memo[(n, m)] = -float('inf')
        return -float('inf')
    
    res = -float('inf')
    for i in range(3):
        res = max(res, A[-n + i] + sub_max(n - i - 2, m - 1))
    memo[(n, m)] = res
    return res

print(sub_max(N, N//2))
# print(memo)