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 = [-10**15]*(n+1)
    dp[2] = max(a[0], a[1])
    if n > 2:
        dp[3] = max(a[:3])
        aa = a[0]+a[2]
        for i in range(4, n+1):
            if i%2:
                aa += a[i-1]
                dp[i] = max(dp[i-1], dp[i-2]+a[i-1])
            else:
                dp[i] = max(aa, dp[i-2]+a[i-1])
    print(dp[n])

if __name__ == "__main__":
    main()