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

stdin = sys.stdin

ns = lambda: stdin.readline().rstrip()
ni = lambda: int(stdin.readline().rstrip())
nm = lambda: map(int, stdin.readline().split())
nl = lambda: list(map(int, stdin.readline().split()))

n = ni()
a = nl()
dp = [[0]*3 for _ in range(n+5)]
t = n%2
for i in range(n):
    dp[i][0] = dp[i-2][0] + a[i]
    dp[i][1] = max(dp[i-2][1], dp[i-3][0]) + a[i]
    if t:
        dp[i][2] = max(dp[i-2][2], dp[i-3][1], dp[i-4][0]) + a[i]
if t:
    print(max(dp[n-3][0], dp[n-2][1], dp[n-1][2]))
else:
    print(max(dp[n-2][0], dp[n-1][1]))
