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)

import sys

def solve():
    input = sys.stdin.readline
    N = int(input())
    A = [int(a) for a in input().split()]
    if N % 2 == 0:
        if N == 2: print(max(A))
        else:
            DP = [[-10 ** 20, -10 ** 20] for _ in range(N)]
            DP[0][0] = A[0]
            DP[1][1] = A[1]
            for i in range(2, N):
                DP[i][0] = max(DP[i][0], DP[i-2][0] + A[i])
                DP[i][1] = max(DP[i][1], DP[i-2][1] + A[i])
                if i > 2: DP[i][1] = max(DP[i][1], DP[i-3][0] + A[i])
            print(max(DP[N-2][0], DP[N-1][1]))
    else:
        DP = [[-10**20, -10**20, -10**20] for _ in range(N)]
        DP[0][0] = A[0]
        DP[1][1] = A[1]
        DP[2][2] = A[2]
        DP[2][0] = A[0] + A[2]
        for i in range(3, N):
            DP[i][0] = max(DP[i-2][0] + A[i], DP[i][0])
            DP[i][1] = max(DP[i-2][1] + A[i], DP[i][1])
            DP[i][2] = max(DP[i-2][2] + A[i], DP[i][2])
            if i > 2: 
                DP[i][1] = max(DP[i][1], DP[i-3][0] + A[i])
                DP[i][2] = max(DP[i][2], DP[i-3][1] + A[i])
        ans = max(DP[N-1][2], DP[N-2][1])
        ans = max(ans, DP[N-3][0])

        print(ans)

    return 0

if __name__ == "__main__":
    solve()