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
INF = 10 ** 15
N = int(input())
A = list(map(int,input().split()))
dp_take = defaultdict(lambda: -INF)
dp_not = defaultdict(lambda: -INF)
dp_take[(0,0)] = 0
dp_not[(0,0)] = 0

for i in range(N):
    for j in range((i + 1) // 2 - 1, (i + 2) // 2 + 1):
        if j > 0:
            dp_take[(i+1, j)] = max(dp_take[(i+1, j)], dp_not[(i, j-1)] + A[i])
        dp_not[(i+1, j)] = max(dp_not[(i, j)], dp_take[(i, j)])

print(max(dp_take[(N, N//2)], dp_not[(N, N//2)]))