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: Memory Limit Exceeded)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)

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

SUM=[0]*(N+1)
for i in range(N-1,-1,-1):
    SUM[i]=SUM[i+1]

    if (N-i)%2==1:
        SUM[i]+=A[i]

#print(SUM)
        
from functools import lru_cache
@lru_cache(maxsize=None)
def calc(i,select):
    rest=N-i

    if rest==0 or select==0:
        return 0

    if rest%2==1 and rest//2+1==select:
        return SUM[i]
    
    elif rest%2==0 and rest//2==select:
        return max(calc(i+1,select),A[i]+calc(i+2,select-1))

    elif rest%2==1 and rest//2==select:
        return max(calc(i+1,select),A[i]+calc(i+2,select-1))

print(calc(0,N//2))