As you might already know, Ada the Ladybug is a farmer. She grows many vegetables. During past months, her crop was attacked by colony of parasites. Each vegetable was attacked by A_i parasites. Ada has only limited answer for this. She bought a few bottles with Primal Fear, which is a mixture against parasites.

Primal Fear works in following way: Each Primal Fear bottle has a power assigned to it (which is coincidentally a prime number). If it is applied to a vegetable with N parasites on it, either the N is divisible by its power, then the size of colony is reduced to N/power, or - if the size is not divisible - then it has no effect. Also, as soon as you apply mixture against a colony, the rest of colony will become immune against Primal Fear.

Ada didn't know what to buy so she bought one bottle of every possible power. Can you find out the best strategy to fight against parasites?

Input

The first line of input will contain 1 ≤ N ≤ 1000, the number of vegetable.

The line will contain N numbers 1 ≤ A_i ≤ 2000, the size of colony on i^th vegetable.

Output

Print the minimum sum of sizes of colonies which could be achieved after applying Primal Fear optimally.

Example Input

3
2 8 6

Example Output

8

Example Input

4
6 6 6 6

Example Output

17

Example Input

3 
7 4 22

Example Output

5

Example Input

3
11 22 17

Example Output

13

Example Input

2
77 11

Example Output

12