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
#f dp
n = int(input())
a = list(map(int, input().split()))
DIM, PER = 0, 1
MIN, MAJ = 0, 1
# pick from 0~i
# j = DIM or PER if i is odd, MIN or MAJ otherwise
dp = [[None, None] for _ in range(n)]
dp[0] = [0, a[0]]
dp[1] = [0, max(a[0], a[1])]
for i in range(2, n):
    if i % 2 == 0:
        dp[i][MIN] = max(dp[i - 2][MIN] + a[i], dp[i - 1][PER])
        dp[i][MAJ] = dp[i - 2][MAJ] + a[i]
    else:
        dp[i][DIM] = max(dp[i - 2][DIM] + a[i], dp[i - 1][MIN])
        dp[i][PER] = max(dp[i - 2][PER] + a[i], dp[i - 1][MAJ])
if n % 2 == 0:
    print(dp[n - 1][PER])
else:
    print(dp[n - 1][MIN])