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
from math import gcd
from functools import reduce
 
n=int(input())
ar=list(map(int,input().split(' ')))
 
dp=[[-(10**20)]*6 for i in range(n+5)]+[[0]+[-(10**20)]*8 for i in range(3)]
 
 
#1> 2 3> 4  6> 7 8> 9 10 11> 12> 14
def cn(z,j):
	return (z-j+1)//2
ans=-(10**20)
for i in range(n):
	idx=int(i)
	dp[idx]=dp[idx-2].copy()
	for j in range(0,5):
			for k in range(j+1):
					dp[idx][j]=max(dp[idx][j],dp[idx-k-2][j-k])
	for j in range(5):
		dp[i][j]+=ar[i]
		if cn(i+1,j)==n//2:
			ans=max(ans,dp[i][j])
print(ans)

