#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

Int n;
Int s[108000];
Int ss[108000];
Int ans = 0;
int main(){
    cin >> n;
    for(int i = 0;i < n;i++){
        cin >> s[i];
    }

    for(int d = 1;d < n;d++){
        Int tmp = 0;
        for(int kd = 0;kd < n-1;kd += d){
            int op = n-1 - kd;
            if(op <= kd && op % d == 0)break;
            tmp += s[kd] + s[op];
            if(op > d)
                ans = max(ans, tmp);
        }
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

Int n;
Int s[108000];
Int ss[108000];
Int ans = 0;
int main(){
    cin >> n;
    for(int i = 0;i < n;i++){
        cin >> s[i];
    }

    for(int d = 1;d < n;d++){
        Int tmp = 0;
        for(int kd = 0;kd < n-1;kd += d){
            int op = n-1 - kd;
            if(op <= kd && op % d == 0)break;
            tmp += s[kd] + s[op];
            if(op > d)
                ans = max(ans, tmp);
        }
    }
    cout << ans << endl;
    return 0;
}
```