#include <bits/stdc++.h>
using namespace std;

int N, A[1 << 20], C[1 << 20];
long long ans = 0;

int main() {
	cin >> N;
    for(int i = 0;i < N;i++) {
      cin >> A[i];
    }

    for(int c = 1;c < N;c++) {
      
      int l = 0, r = N-1;
      long long tans = 0;
      while(l < N) {
        C[l]++;C[r]++;
        if(C[l] > 1 || C[r] > 1) {
           break;
        }
        tans += A[l] + A[r];
        if(N - 1 - l  > c) {
        	ans = max(ans, tans);
        }
        l += c;
        r -= c;
      }
     
      l= 0; r =N-1;
      while ( l<N) {
       C[l] =C[r] = 0;
       l += c;
       r -= c;
      }
    }
    cout << ans;
	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 <bits/stdc++.h>
using namespace std;

int N, A[1 << 20], C[1 << 20];
long long ans = 0;

int main() {
	cin >> N;
    for(int i = 0;i < N;i++) {
      cin >> A[i];
    }

    for(int c = 1;c < N;c++) {
      
      int l = 0, r = N-1;
      long long tans = 0;
      while(l < N) {
        C[l]++;C[r]++;
        if(C[l] > 1 || C[r] > 1) {
           break;
        }
        tans += A[l] + A[r];
        if(N - 1 - l  > c) {
        	ans = max(ans, tans);
        }
        l += c;
        r -= c;
      }
     
      l= 0; r =N-1;
      while ( l<N) {
       C[l] =C[r] = 0;
       l += c;
       r -= c;
      }
    }
    cout << ans;
	return 0;
}
```