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 Python (3.8.2) (judge verdict: Wrong Answer)

n=int(input())
a=list(map(int,input().split()))
#n=100001
#a=list(range(n))
import numpy as np
dp=np.zeros((3,n+1),np.int64)
dp[:,0]=0
dp[1,1]=a[0]
for i in range(2,n+1):
    l,r=max(1,n//2-(n-i+1)//2-1),min(n,i//2+2)
    if i%3==2:
      now,pre,prepre=2,1,0
    elif i%3==0:
      now,pre,prepre=0,2,1
    elif i%3==1:
      now,pre,prepre=1,0,2
    dp[now,l:r]=np.maximum(dp[pre,l:r],dp[prepre,l-1:r-1]+a[i-1])
print(dp[now,n//2])