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<iostream>
#include<vector>
using namespace std;
using ll = long long;
int main(){
    int n;
    cin >> n;
    vector<ll> a(n);
    for(auto &e : a)cin >> e;
    vector<ll> dp(n+1);
    ll sum = a[0]; 
    for(int i = 2 ; i <= n ; i++){
        if(i % 2 == 0) {
            dp[i] = max(a[i-1] + dp[i-2], sum);
        } 
        else {
            dp[i] = max(a[i-1] + dp[i-2], dp[i-1]);
            sum += a[i-1];
        }
    }
    cout << dp[n] << endl;
    return 0;
}