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.

Examples

Input

6
1 2 3 4 5 6


Output

12


Input

5
-1000 -100 -10 0 10


Output

0


Input

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


Output

5000000000


Input

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


Output

295
/**
 *     author: qodjf
 *     created: 04.18.2020 02:04:55
 */
#include <vector>
#include <cmath>
#include <iostream>
using namespace std;

using ll = long long;

int main() {
  int N;
  cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  vector<ll> dp(N + 10, 0);

  ll sum = 0;
  for (int i = N - 1; i >= 1; i -= 2) {
    sum += a[i];
    dp[i - 1] = max(a[i - 1] + dp[i + 1], sum);
  }
  for (int i = N - 3; i >= 0; i -= 2) {
    dp[i] = max(dp[i + 2] + a[i], dp[i + 1]);
  }
  cout << dp[0] << endl;
}
