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>
#define rep(i,a,b) for(ll i=ll(a);i<ll(b);i++)
using ll=long long;
using namespace std;
ll a[220000],x[220000],y[220000];
int main(){
    ll n;
    cin>>n;
    rep(i,0,n)cin>>a[i];
    rep(i,0,n)x[i]=(i>1?x[i-2]:0)+a[i];
    rep(i,1,n){
        if(i%2==0)y[i]=max(y[i-1],(i>2?y[i-2]:0)+a[i]);
        else y[i]=max(x[i-1],(i>2?y[i-2]:0)+a[i]);
    }
    cout<<y[n-1];
}