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
input = lambda: sys.stdin.readline().rstrip("\r\n")

def solve():
    n = int(input())
    a = [int(x) for x in input().split()]

    from collections import defaultdict

    dp = defaultdict(lambda : -float('inf'))
    dp[(0, 0, 0)] = 0

    for i in range(1, n + 1):
        max_j = i//2 if i % 2 == 0 else i//2 + 1
        min_j = n//2 - (n - i)//2 if (n - i) % 2 == 0 else n//2 - ((n - i)//2 + 1)
        for j in range(min_j, max_j + 1):
            dp[(i, j, 0)] = max(dp[(i - 1, j, 0)], dp[(i - 1, j, 1)])
            dp[(i, j, 1)] = dp[(i - 1, j - 1, 0)] + a[i - 1]
    print(max(dp[(n, n//2, 0)], dp[(n, n//2, 1)]))
solve()