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()))
inf = 10**18

x = N % 2 + 1
dp = [[-inf] * 4 for _ in range(N + 10)]
dp[0][0] = 0
for i, a in enumerate(A):
    for j in range(x + 1):
        dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j])
        now = dp[i][j]
        if (i + j) % 2 == 0:
            now += a
        dp[i + 1][j] = max(dp[i + 1][j], now)

print(dp[N][x])