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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"

#define rep(i, a) for (int i = 0; i < (a); ++i)
#define REP(i, a, b) for (int i = a; i < (b); ++i)

#define vi vector<int>

#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1) cerr << #x1 << ": " << x1 << endl
#define debug_2(x1, x2) cerr << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << endl
#define debug_3(x1, x2, x3) cerr << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " << x3 << endl
#define debug_4(x1, x2, x3, x4) cerr << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " << x3 << ", " #x4 << ": " << x4 << endl
#define debug_5(x1, x2, x3, x4, x5) cerr << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " << x3 << ", " #x4 << ": " << x4 << ", " #x5 << ": " << x5 << endl
#define debug(...) CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~)) (__VA_ARGS__)

using namespace std;
using ll = long long;
using P = pair<int, int>;

void Main() {
  int n;
  cin>>n;
  vector<ll> a(n);
  rep(i, n) cin>>a[i];
  vector<ll> sum(n), dp(n+1);
  rep(i, n) {
    if(i&1) sum[i]=sum[i-1];
    else sum[i]=sum[i-1]+a[i];
  }
  REP(i, 1, n) {
    if(i&1) dp[i+1]=max(dp[i-1]+a[i],sum[i-1]);
    else dp[i+1]=max(dp[i-1]+a[i],dp[i]);
  }
  cout<<dp[n]<<endl;
}

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(15);
  Main();
  return 0;
}