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
n = int(input())
a = list(map(int, input().split()))

dp = [dict() for _ in range(n)]

dp[0][0] = 0
dp[0][1] = a[0]
dp[1][0] = 0
dp[1][1] = max(a[0], a[1])

import math
for i in range(2, n):
    k1 = int(math.ceil((i + 1) / 2))
    k2 = k1 - 1

    if i % 2 == 0:
        dp[i][k1] = dp[i-2][k1-1] + a[i]
    else:
        dp[i][k1] = max(dp[i-1][k1], dp[i-2][k1-1] + a[i])

    dp[i][k2] = max(dp[i-1][k2], dp[i-2][k2-1] + a[i])

print(dp[-1][n // 2])
