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: Time Limit Exceeded)

def main():
    import sys
    input = sys.stdin.readline
    n=int(input())
    a=list(map(int,input().split()))
    indices=[*range(len(a))]
    sorted_indices=sorted(indices,key=lambda i: -a[i])
    sorted_num= [a[i] for i in sorted_indices]
    #print(sorted_indices)
    #print(sorted_num)
    residue=n//2
    dif=[]
    ans=0
    for i in range(n):
        if residue==0: break
        flg=False
        for j in range(len(dif)):
            if abs(sorted_indices[i]-dif[j])==1:
                flg=True
        if flg: continue
        
        dif.append(sorted_indices[i])
        ans+=sorted_num[i]
        residue-=1
    #print(dif)
    print(ans)
        
    
    
if __name__ == '__main__':
    main()