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() {
  int n;
  cin>>n;
  long long a[n],b[n],c[n];
  for(int i=0;i<n;i++){
    long long k;
    cin>>k;
    a[i]=k;
  }
  b[0]=0;
  b[1]=max(a[0],a[1]);
  c[0]=a[0];
  c[1]=b[1];
  b[2]=max(b[1],a[2]);
  c[2]=a[0]+a[2];
  for(int i=3;i<n;i++){
    if(i%2==1){
      b[i]=max(a[i]+b[i-2],a[i-1]+c[i-3]);
      c[i]=b[i];
    }
    else {
      b[i]=max(max(c[i-2],a[i-1]+b[i-3]),a[i]+b[i-2]);
      c[i]=c[i-2]+a[i];
    }
  }
  cout<<b[n-1]<<endl;
}
