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
sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))
from collections import defaultdict
def resolve():
    N = ir()
    A = lr()
    dp = defaultdict(lambda: -float('inf'))
    dp[0, 0, 0] = 0
    for i in range(N):
        for j in range(max(i//2-1, 0), i//2+2):
            dp[i+1, j+1, 1] = dp[i, j, 0]+A[i]
            dp[i+1, j, 0] = max(dp[i, j, 0], dp[i, j, 1])
    # print(dp)
    print(max(dp[N, N//2, 1], dp[N, N//2, 0]))
resolve()