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
readline = sys.stdin.readline

N = int(readline())
A = list(map(int, readline().split()))

INF = 10**18
limit = 4
S = (2*limit+3)
dpb = [-INF]*S
dpw = [-INF]*S
dpw[0] = 0
for i in range(N):
    a = A[i]
    dpb2 = [-INF]*S
    dpw2 = [-INF]*S
    for j in range(-limit, limit):
        if -limit <= j - 1 < limit:
            dpw2[j-1] = max(dpw2[j-1], dpb[j], dpw[j])
            dpb2[j-1] = max(dpb2[j-1], dpb[j], dpw[j])
        if -limit <= j + 1 < limit:
            dpb2[j+1] = max(dpb2[j+1], dpw[j]+a)
    dpw = dpw2[:]
    dpb = dpb2[:]

idx = N//2*2 - N
print(max(dpw[idx], dpb[idx]))
    