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
#!/usr/bin/env python3
# coding: utf-8
import collections
def debug(arg):
    if __debug__:
        pass
    else:
        import sys
        print(arg, file=sys.stderr)

def main():
    pass
    N, *A = map(int, open(0).read().split())
    a = dict(enumerate(A, 1))
    dp = collections.defaultdict(lambda: -float("inf"))
    dp[0, 0] = 0 
    dp[1, 0] = 0 
    dp[1, 1] = a[1]
    for i in range(2, N + 1):
        jj = range(max(i // 2 - 1, 1), (i + 1) // 2 + 1)
        for j in jj:
            x = dp[i - 2, j - 1] + a[i]
            y = dp[i - 1, j]
            dp[i, j] = max(x, y)
    print(dp[N, N // 2])

if __name__ == "__main__":
    main()