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 = [0, 0]+list(map(int, input().split()))+[0, 0]
skip = N-2*(N//2)+1
dp = [[-10**18]*(skip+1) for _ in range(N+4)]

for i in range(2):
    for j in range(skip+1):
        dp[i][j] = 0

for i in range(2, N+4):
    for j in range(skip+1):
        dp[i][j] = max(dp[i][j], dp[i-2][j]+A[i])
        
        if i>=3 and j+1<=skip:
            dp[i][j+1] = max(dp[i][j+1], dp[i-3][j]+A[i])
        
        if i>=4 and j+2<=skip:
            dp[i][j+2] = max(dp[i][j+2], dp[i-4][j]+A[i])

print(dp[N+3][skip])