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 -*-

# F - Select Half

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

# memo[i][m] a[0:i+1]からm個選ぶときの最大値
memo = [{} for i in range(n)]
memo[0] = {0: 0, 1: a[0]}
memo[1] = {1: max(a[:2])}

for i in range(2, n):
    m = (i + 1) // 2
    memo[i][m] = max(memo[i - 1][m], memo[i - 2][m - 1] + a[i])
    if i % 2 == 0:
        memo[i][m + 1] = memo[i - 2][m] + a[i]

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