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: Wrong Answer)

import sys

# import bisect
# from collections import Counter, deque, defaultdict
# import copy
# from heapq import heappush, heappop, heapify
# import itertools
# from operator import attrgetter, itemgetter
# import math

# from numba import jit
# import numpy as np

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    n = int(input())
    a = [0] + list(map(int, readline().split()))

    if n % 2 == 0:
        ans1 = sum(a[::2])
        ans2 = sum(a[1::2])
        print(max(ans1, ans2))
        sys.exit()

    dp = [[0] * 2 for _ in range(n + 1)]

    # 普通に選ぶ場合
    dp[1][0] = 0
    dp[2][0] = max(a[1], a[2])
    dp[3][0] = max(a[1], a[2], a[3])

    # 1個多く選ぶ場合（奇数個のみ）
    dp[1][1] = a[1]
    dp[3][1] = a[1] + a[3]

    i = 4

    while i < n + 1:
        cur1 = a[i]

        # 偶数だよ
        dp[i][0] = max(dp[i - 1][1], dp[i - 2][0] + cur1)

        i += 1
        cur2 = a[i]

        # 奇数だよ
        dp[i][0] = max(dp[i - 2][0] + cur2, dp[i - 3][0] + cur2, dp[i - 1][0], dp[i - 2][1])
        dp[i][1] = dp[i - 2][1] + cur2

        i += 1

    print(dp[n][0])


if __name__ == '__main__':
    main()