Problem Statement

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.

Sample Input 1

5
0 2 5 1 0

Sample Output 1

3

If you choose A = 3 and B = 2, the game proceeds as follows:

• Move to coordinate 0 + 3 = 3. Your score increases by s_3 = 1.
• Move to coordinate 3 - 2 = 1. Your score increases by s_1 = 2.
• Move to coordinate 1 + 3 = 4. The game ends with a score of 3.

There is no way to end the game with a score of 4 or higher, so the answer is 3. Note that you cannot land the lotus at coordinate 2 without drowning later.

Sample Input 2

6
0 10 -7 -4 -13 0

Sample Output 2

0

The optimal strategy here is to land the final lotus immediately by choosing A = 5 (the value of B does not matter).

Sample Input 3

11
0 -4 0 -99 31 14 -15 -39 43 18 0

Sample Output 3

59