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
from itertools import accumulate
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))
odd = list(accumulate([0] + A[::2]))
even = list(accumulate([0] + A[::-1][::2]))
ans = max(odd[i] + even[N//2-i] for i in range(N//2+1))
if N % 2 == 1:
    dp = [0] * (N//2+1)
    for i in range(0, N-1, 2):
        dp[i//2+1] = max(odd[i//2+1], dp[i//2] + A[i+1])
    ans2 = max(dp[i] + even[N//2-i] for i in range(N//2+1))
    ans = max(ans, ans2)
print(ans)