#include <bits/stdc++.h>
using namespace std;
int n,a[100001],x[100001];
long long ans;
int main() {
    cin>>n;
    for (int i=0; i<n; i++) cin>>a[i];
    for (int i=1; i<n-1; i++) { //i is jump length (a-b)
        long long cur=0;
        int l=0,r=n-1;
        while (l!=r and i<r and l<n-1 and x[r]!=i and x[l]!=i) {
            cur+=a[l]; cur+=a[r];
            x[l]=i; x[r]=i;
            l+=i; r-=i;
            ans=max(ans,cur);
        }
    }
    cout<<ans<<'\n';
}
/*
*/
### Prompt

Construct a CPP code solution to the problem outlined:

There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written.

You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows:

* 1. Choose positive integers A and B. Your score is initially 0.
* 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y.
* If y = N-1, the game ends.
* If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.
* If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.
* 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y.
* If y = N-1, the game ends.
* If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.
* If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.
* 4. Go back to step 2.



You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B?

Constraints

* 3 \leq N \leq 10^5
* -10^9 \leq s_i \leq 10^9
* s_0=s_{N-1}=0
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
s_0 s_1 ...... s_{N-1}


Output

Print the score obtained by the optimal choice of A and B.

Examples

Input

5
0 2 5 1 0


Output

3


Input

6
0 10 -7 -4 -13 0


Output

0


Input

11
0 -4 0 -99 31 14 -15 -39 43 18 0


Output

59

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n,a[100001],x[100001];
long long ans;
int main() {
    cin>>n;
    for (int i=0; i<n; i++) cin>>a[i];
    for (int i=1; i<n-1; i++) { //i is jump length (a-b)
        long long cur=0;
        int l=0,r=n-1;
        while (l!=r and i<r and l<n-1 and x[r]!=i and x[l]!=i) {
            cur+=a[l]; cur+=a[r];
            x[l]=i; x[r]=i;
            l+=i; r-=i;
            ans=max(ans,cur);
        }
    }
    cout<<ans<<'\n';
}
/*
*/
```