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: Runtime Error)

import sys
IS = lambda: sys.stdin.readline().rstrip()
II = lambda: int(IS())
MII = lambda: list(map(int, IS().split()))
from bisect import bisect_left, insort_left

def main():
    n = II()
    aa = MII()
    index = [i for i in range(n)]
    aa = list(zip(index, aa))
    aa.sort(key=lambda x: x[1], reverse=True)
    sumv = 0
    cnt = 0
    neibs = [-100]
    u = n//2
    i = 0
    while cnt < u:
        idx = aa[i][0]
        d = bisect_left(neibs, idx)
        if d-1<0:
            l = -10
            r = -10
        else:
            l = neibs[d-1] if d != 1 else -10
            r = neibs[d] if len(neibs) != d else neibs[d-1]
        if l == idx-1 or l == idx+1 or r == idx-1 or r == idx+1:
            i+=1; continue
        sumv += aa[i][1]
        insort_left(neibs, idx)
        cnt += 1
        i += 1
    print(sumv)


if __name__ == '__main__':
    main()