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
def main():
    N = int(input())
    A = list(map(int, input().split()))
    dp = [[-1 * pow(10, 15)] * 3 for _ in range(N)]
    if N == 2:
        return max(A)
    dp[0][0] = A[0]
    dp[1][1] = A[1]
    dp[2][2] = A[2]
    for i in range(N):
        if i < 2:
            continue
        dp[i][0] = dp[i-2][0] + A[i]
        if i < 3:
            continue
        dp[i][1] = max(dp[i-3][0], dp[i-2][1]) + A[i]
        if i < 4:
            continue
        dp[i][2] = max(dp[i-4][0], dp[i-3][1], dp[i-2][2]) + A[i]
    if N % 2 == 0:
        return max(dp[-1][1], dp[-2][0])
    else:
        return max(dp[-1][2], dp[-2][1], dp[-3][0])
print(main())
