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.
• 1. 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.
• 1. 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.
• 1. 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

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