JOIN

 Problem Statement

Problem Statement for EllysCoprimesDiv2

### Problem Statement

Elly has a set of unique positive integers, given in the int[] numbers. She wants to add several (possibly none) new positive integers to this set, such that when the set is sorted no two consecutive numbers will share a positive divisor greater than 1. Return the smallest possible count of new numbers, with which she can achieve that.

### Definition

 Class: EllysCoprimesDiv2 Method: getCount Parameters: int[] Returns: int Method signature: int getCount(int[] numbers) (be sure your method is public)

### Constraints

-numbers will contain between 1 and 50 elements, inclusive.
-Each element of numbers will be between 1 and 100,000, inclusive.
-All elements of numbers will be distinct.

### Examples

0)

 `{2200, 42, 2184, 17}`
`Returns: 3`
 Here one possible set of additional numbers is {43, 2195, 2199}. The sorted sequence is (17, 42, 43, 2184, 2195, 2199, 2200), and as you may see, no two consecutive numbers share a divisor greater than one.
1)

 `{13, 1, 6, 20, 33}`
`Returns: 0`
 For some sets, such as this one, no additional numbers are needed. When sorted, no pair of consecutive numbers shares a common divisor greater than 1.
2)

 `{7, 42}`
`Returns: 1`
 Note that prime numbers are not coprime with all other numbers.
3)

 ```{55780, 44918, 55653, 4762, 41536, 40083, 79260, 7374, 24124, 91858, 7856, 12999, 64025, 12706, 19770, 71495, 32817, 79309, 53779, 8421, 97984, 34586, 893, 64549, 77792, 12143, 52732, 94416, 54207, 51811, 80845, 67079, 14829, 25350, 22976, 23932, 62273, 58871, 82358, 13283, 33667, 64263, 1337, 42666}```
`Returns: 15`
 Large random set of numbers.

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.

This problem was used for:
Single Round Match 577 Round 1 - Division II, Level Three