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 collections import defaultdict

N = int(input())
*A, = map(int, input().split())
INF = 10**20
dp = defaultdict(lambda :-INF)
dp[(0,0,0)] = 0

for i in range(1, N+1):
    for j in range(i//2-1, i//2+2):
        dp[1,i,j] = dp[0,i-1,j-1]+A[i-1]
        dp[0,i,j] = max(dp[1,i-1,j], dp[0,i-1,j])

ans = max(dp[1,N,N//2], dp[0,N,N//2])
print(ans)
