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: Accepted)

import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7 # 998244353
input=lambda:sys.stdin.readline().rstrip()
def resolve():
    n = int(input())
    A = list(map(int,input().split()))

    if n & 1 == 0:
        res = -INF
        score = sum(A[::2])
        res = max(res, score)
        for i in range(n-1,-1,-1):
            if i & 1:
                score += A[i]
            else:
                score -= A[i]
                res = max(res, score)
        print(res)
        return

    front_dp = [None] * n
    choose = -INF
    not_choose = 0
    for i in range(1, n, 2):
        choose, not_choose = max(choose, not_choose) + A[i], not_choose + A[i-1]
        front_dp[i] = max(choose, not_choose)

    back_dp = [None] * n
    choose = -INF
    not_choose = 0
    for i in range(n-2, -1, -2):
        choose, not_choose = max(choose, not_choose) + A[i], not_choose + A[i+1]
        back_dp[i] = max(choose, not_choose)

    res = -INF
    for i in range(1, n, 2):
        if i + 2 < n:
            res = max(res, front_dp[i] + back_dp[i+2])

    res = max(res, front_dp[-2])
    res = max(res, back_dp[1])

    print(res)
resolve()