Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

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

Sample Output 4

295

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

from collections import defaultdict


def main():
    N = int(input())
    A = list(map(int, input().split()))

    def default():
        return -float("inf")
    dp = [defaultdict(default) for _ in range(N)]
    dp[0][0] = 0
    dp[0][1] = A[0]
    dp[1][0] = 0
    dp[1][1] = max(A[0], A[1])
    for i in range(2, N):
        dp[i][i//2] = max(dp[i-2][i//2-1] + A[i], dp[i-1][i//2])
        dp[i][i//2+1] = max(dp[i-2][i//2] + A[i], dp[i-1][i//2+1])
    print(dp[N-1][N//2])


if __name__ == "__main__":
    main()