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 = tuple(map(int, input().split()))

if(n <= 3):
    print(max(a))
    exit()

dp = [[0] * 2 for _ in range(n+1)]
dp[1][1] = a[0]
dp[2][1] = a[1]
dp[3][0] = a[2]
dp[3][1] = a[0] + a[2]

for i in range(4,n+1):
    if(i%2 == 0):
        dp[i][1] = a[i-1] + max(dp[i-2][1], dp[i-3][1])
    else:
        dp[i][0] = a[i-1] + max(dp[i-2][0], dp[i-3][1], dp[i-4][1])
        dp[i][1] = a[i-1] + dp[i-2][1]

if(n%2==0):
    ans = max(dp[-1][1], dp[-2][1])
else:
    ans = max(dp[-1][0], dp[-2][1], dp[-3][1])

print(ans)