#include<iostream>
#include<vector>
#include<cstdint>
#include<algorithm>

template<class T>
void chmax(T &l, const T &r) {
  l = std::max(l, r);
}

int main() {
  using i64 = std::int_fast64_t;

  int n;
  std::cin >> n;
  std::vector<i64> s(n);
  for (auto &e : s) std::cin >> e;
  n -= 1;

  i64 ans = 0;
  
  for (int d = 1; d != n; d += 1) {
    i64 pre = 0;
    i64 suf = 0;
    for (int i = 0;; i += 1) {
      if (i * d > n || n - i * d <= d) break;
      if (n % d == 0 && i * d >= n - i * d) break;
      pre += s[i * d];
      suf += s[n - i * d];
      chmax(ans, pre + suf);
    }
  }

  std::cout << ans << "\n";
}

### Prompt

Generate 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<iostream>
#include<vector>
#include<cstdint>
#include<algorithm>

template<class T>
void chmax(T &l, const T &r) {
  l = std::max(l, r);
}

int main() {
  using i64 = std::int_fast64_t;

  int n;
  std::cin >> n;
  std::vector<i64> s(n);
  for (auto &e : s) std::cin >> e;
  n -= 1;

  i64 ans = 0;
  
  for (int d = 1; d != n; d += 1) {
    i64 pre = 0;
    i64 suf = 0;
    for (int i = 0;; i += 1) {
      if (i * d > n || n - i * d <= d) break;
      if (n % d == 0 && i * d >= n - i * d) break;
      pre += s[i * d];
      suf += s[n - i * d];
      chmax(ans, pre + suf);
    }
  }

  std::cout << ans << "\n";
}

```