#include "bits/stdc++.h"

using namespace std;

void solve()
{
    int n;
    cin >> n;
    vector<long> as(n);
    for (int i = 0; i < n; i++)
    {
        cin >> as[i];
    }
    long ans = 0;
    vector<int> vst(n);
    for (int d = 1; d <= (n - 1) / 2; d++)
    {
        long res = 0;
        fill(vst.begin(), vst.end(), 0);
        for (int k = 0; (k + 1) * d < n; k++)
        {
            int l = k * d, r = n - 1 - l;
            if (vst[l] || vst[r] || l == r)
                break;
            vst[l] = vst[r] = 1;
            res += as[l] + as[r];
            ans = max(ans, res);
        }
    }
    cout << ans << endl;
}

int main()
{
    solve();
    cerr << "\"努力不足ですね！\"" << endl;
    return 0;
}
### Prompt

Your challenge is to write a CPP solution to the following problem:

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;

void solve()
{
    int n;
    cin >> n;
    vector<long> as(n);
    for (int i = 0; i < n; i++)
    {
        cin >> as[i];
    }
    long ans = 0;
    vector<int> vst(n);
    for (int d = 1; d <= (n - 1) / 2; d++)
    {
        long res = 0;
        fill(vst.begin(), vst.end(), 0);
        for (int k = 0; (k + 1) * d < n; k++)
        {
            int l = k * d, r = n - 1 - l;
            if (vst[l] || vst[r] || l == r)
                break;
            vst[l] = vst[r] = 1;
            res += as[l] + as[r];
            ans = max(ans, res);
        }
    }
    cout << ans << endl;
}

int main()
{
    solve();
    cerr << "\"努力不足ですね！\"" << endl;
    return 0;
}
```