#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<ll> vl;
typedef long double ld;
typedef vector<ld> vd;
typedef bool bl;
typedef vector<bl> vb;
typedef unordered_map<ll,unordered_map<ll,ll>> graph;

const ll e5 = 1 << 20;
const ll mod = 1000000007;
const ll e3 = 1 << 13;
const ll INF = 1ll << 60;

ll n;
ll s[e5];
ll b[e5];
ll ans = 0;

int main(){
  cin >> n;
  for(ll i = 0;i < n;i++) cin >> s[i];
  for(ll i = 1;i <= n;i++){
    ll mem1 = 0;
    ll mem2 = 0;
    unordered_set<ll> r;
    unordered_set<ll> l;
    for(ll j = 0,k = n-1;k >= i;j+=i,k-=i){
      r.insert(j);
      l.insert(k);
      if(r.count(k) || l.count(j)) continue;
      mem1 += s[j];
      mem2 += s[k];
      ans = max(ans,mem1+mem2);

    }
  }
  cout << ans << endl;

}

### 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;

typedef long long ll;
typedef vector<ll> vl;
typedef long double ld;
typedef vector<ld> vd;
typedef bool bl;
typedef vector<bl> vb;
typedef unordered_map<ll,unordered_map<ll,ll>> graph;

const ll e5 = 1 << 20;
const ll mod = 1000000007;
const ll e3 = 1 << 13;
const ll INF = 1ll << 60;

ll n;
ll s[e5];
ll b[e5];
ll ans = 0;

int main(){
  cin >> n;
  for(ll i = 0;i < n;i++) cin >> s[i];
  for(ll i = 1;i <= n;i++){
    ll mem1 = 0;
    ll mem2 = 0;
    unordered_set<ll> r;
    unordered_set<ll> l;
    for(ll j = 0,k = n-1;k >= i;j+=i,k-=i){
      r.insert(j);
      l.insert(k);
      if(r.count(k) || l.count(j)) continue;
      mem1 += s[j];
      mem2 += s[k];
      ans = max(ans,mem1+mem2);

    }
  }
  cout << ans << endl;

}

```