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,collections as cl,bisect as bs
sys.setrecursionlimit(100000)
input = sys.stdin.readline
mod = 10**9+7
Max = sys.maxsize
def l(): #intのlist
    return list(map(int,input().split()))
def m(): #複数文字
    return map(int,input().split())
def onem(): #Nとかの取得
    return int(input())
def s(x): #圧縮
    a = []
    if len(x) == 0:
        return []
    aa = x[0]
    su = 1
    for i in range(len(x)-1):
        if aa != x[i+1]:
            a.append([aa,su])
            aa = x[i+1]
            su = 1
        else:
            su += 1
    a.append([aa,su])
    return a
def jo(x): #listをスペースごとに分ける
    return " ".join(map(str,x))
def max2(x): #他のときもどうように作成可能
    return max(map(max,x))
def In(x,a): #aがリスト(sorted)
    k = bs.bisect_left(a,x)
    if k != len(a) and a[k] ==  x:
        return True
    else:
        return False

def pow_k(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

"""
def nibu(x,n,r):
    ll = 0
    rr = r
    while True:
        mid = (ll+rr)//2

    if rr == mid:
        return ll
    if (ここに評価入れる):
        rr = mid
    else:
        ll = mid+1
"""
n = onem()
a = l()


if n % 2 == 0:
    po = [a[i] for i in range(n)]
    
    for i in range(n-3,-1,-1):
        po[i] += po[i+2]

    ans = - Max
    co = 0
    for i in range(0,n,2):
        if i + 2 <= n-1:
            ans = max(ans,co+po[i+1],co+po[i+2])
        elif i+1 <= n-1:
            ans = max(ans,co+po[i+1])
        else:
            ans = max(ans,co+0)
        co += a[i]
    co = 0
    for i in range(1,n,2):
        if i + 1 <= n-1:
            ans = max(ans,co+po[i+1])
        else:
            ans = max(ans,co+0)
        co += a[i]
    print(ans)

else:
    po = [a[i] for i in range(n)]
    mi = [-Max for i in range(n)]
    
    for i in range(n-3,-1,-1):
        po[i] += po[i+2]
    ans =  sum(a[1::2])
    #print(ans)
    l1 = [-Max for i in range(n)]
    for i in range(n):
        if i != n-1:
            l1[i] = po[i+1]

    """
    co = 0
    for i in range(0,n,2):
        if i != n-1:
            l1[i] = co + po[i+1]
        else:
            l1[i] = co
        co += a[i]
    co = 0
    for i in range(1,n,2):
        if i != n-1:
            l1[i] = co + po[i+1]
        else:
            l1[i] = co
        co += a[i]
    """

    for i in range(n-1,-1,-1):
        if i == n-1:
            continue
        elif i == n-2:
            mi[i] = l1[i]
        else:
            mi[i] = max(mi[i+2]+a[i],l1[i])


    l1 = mi


    """
    for i in range(n-1,-1,-1):
        if i <= n-3:
            mi[i] = min(mi[i+2],a[i])
        else:
            mi[i] = a[i]
    print(mi)
    """
    
    l2 = [-Max for i in range(n)]
    
    for i in range(n-1,-1,-1):
        l2[i] = po[i]
        
    #print(l1)
    #print(l2)
    co = 0

    for i in range(0,n,2):
        if i + 2 <= n-1:
            #print(ans,co+l1[i+1],co+l2[i+2])
            ans = max(ans,co+l1[i+1],co+l2[i+2])
        elif i+1 <= n-1:
            ans = max(ans,co+l1[i+1])
        else:
            ans = max(ans,co)
        
        co += a[i]
    co = 0
    #print(ans)
    for i in range(1,n,2):
        #print(ans,co+l1[i+1])
        ans = max(ans,co+po[i+1])
        #ans = max(ans,co+l1[i+1])
        co += a[i]
    #print("po:"+str(mi[1]))
    print(ans)