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)

def main():
    N = int(input())
    A = [int(i) for i in input().split()]
    if N % 2 == 0:
        dp = [[0]*2 for _ in range(N//2 + 1)]
        for i in range(N//2):
            dp[i+1][0] = dp[i][0] + A[2*i]

            dp[i+1][1] = max(dp[i][0], dp[i][1]) + A[2*i+1]

        print(max(dp[-1]))
    else:
        dp = [[0]*3 for _ in range(N//2 + 1)]
        for i in range(N//2):
            dp[i+1][0] = dp[i][0] + A[2*i]

            dp[i+1][1] = max(dp[i][0], dp[i][1]) + A[2*i+1]

            dp[i+1][2] = max(dp[i][0], dp[i][1], dp[i][2]) + A[2*i+2]

        print(max(dp[-1]))


if __name__ == '__main__':
    main()