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
#include<algorithm>
#include<iostream>
#include<vector>

using i64 = long long;

int main() {
  int n;
  std::cin >> n;
  int m = n / 2;
  int t = n - m * 2 + 2;
  std::vector<i64> a(n);
  for (auto &e : a) std::cin >> e;
  std::vector<i64> dp_(t + 1, 0);
  const auto dp = dp_.begin() + 1;
  dp[-1] = -10000000000000000;
  for (int i = 0; i < m; i += 1) {
    for (int j = 0; j < t; j += 1) {
      dp[j] = std::max(dp[j] + a[2 * i + j], dp[j - 1]);
    }
  }
  std::cout << dp[t - 1] << "\n";
}
  