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<bits/stdc++.h>
using namespace std;

int main() {
  using LL = long long;

  int N;
  cin >> N;
  vector<LL> A(N);
  for(auto& i: A) cin >> i;

  const LL NG = -1e18;
  vector<map<int, LL>> memo(N);
  function<LL(int,int)> dfs = [&](int i, int n) {
    if(n == 0) return 0ll;
    if(N <= i) return NG;
    if(N < i+2*n-1) return NG;
    if(memo[i][n]) return memo[i][n];
    return memo[i][n] = max(dfs(i+1, n), A[i]+dfs(i+2, n-1));
  };

  cout << dfs(0, N/2) << endl;
}
