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
sys.setrecursionlimit(2000000000)
N = int(input())
import math
l = [int(x) for x in input().split()]
tobi = [0]*(math.ceil(N/2))
tobi[0] = l[0]
for i in range(1,math.ceil(N/2)):
    tobi[i] = tobi[i-1] + l[i*2]
from functools import lru_cache
@lru_cache(maxsize=1000000000)
def motomeru(x,y):
    if y == 0 or x == 0 or x == 1:
        return 0
    elif x % 2 == 0:
        return max(motomeru(x-2,y-1)+l[x-1],tobi[math.floor((x-1)/2)])
    else:
        return max(motomeru(x-2,y-1)+l[x-1],motomeru(x-1,y))
print(motomeru(N,N//2))
