We have N gemstones labeled 1 through N.

You can perform the following operation any number of times (possibly zero).

• Select a positive integer x, and smash all the gems labeled with multiples of x.

Then, for each i, if the gem labeled i remains without getting smashed, you will receive a_i yen (the currency of Japan). However, a_i may be negative, in which case you will be charged money.

By optimally performing the operation, how much yen can you earn?

Constraints

• All input values are integers.
• $1 \leq N \leq 100$
• $|a_i| \leq 10^9$

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum amount of money that can be earned.

Examples

Input

6
1 2 -6 4 5 3

Output

12

Input

6
100 -100 -100 -100 100 -100

Output

200

Input

5
-1 -2 -3 -4 -5

Output

0

Input

2
-1000 100000

Output

99000

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