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)

# coding: utf-8
# Your code here!
from math import floor
def solve(a):
    c=1
    co=len(a)//2
    ar=[]
    for i in range(len(a)):
        ar.append([a[i],i])
    ar.sort(reverse=True)
    x=ar[0][1]
    ss=ar[0][0]
    f=[ss]
    i=1
    #print(ar)
    while c<co and i<len(a):
        y=ar[i][1]
        if abs(y-x)!=1:
            ss+=ar[i][0]
            f.append(ar[i][0])
            x=y 
            c+=1
        i+=1
    print(ss)
n=int(input())
(solve([int(x) for x in input().split()]))