ADACON  Ada and Connections
Ada the Ladybug was on a trip with her friends. They each bought a souvenir there. As all of them are mathematicians, everybody bought a number. They want to modify the numbers to have some connection between each other. They have decided to modify the numbers sou they would have their GCD greater than 1 ( gcd(a_{1},a_{2},a_{3},...,a_{N})>1). Anyway it is not easy to change a number  the only thing they can do is to go to a proffesor in mathematics, which could forge a number A into number A+1 or A1. As this operation is not cheap, they want to minimize number of such operations. A number might be forged any number of times.
NOTE: gcd(a,0)==a (so gcd of two 0 is also 0)
Input
The first line contains an integer 1 ≤ N ≤ 3*10^{5}, the number of friend who were on trip (and also the number of numbers).
The second line contains N integers 0 ≤ a_{i} ≤ 10^{6}
Output
Print a single line with minimum number of operations to make a connection between all numbers.
Example Input
5 3 9 7 6 31
Example Output
2
Example Input 2
9 3 4 5 7 8 9 11 12 13
Example Output 2
6
Example Input 3
5 7 7 11 17 1
Example Output 3
5
hide comments
manya_cod4:
20171218 13:58:32
@morass what is the expected time complexity of this problem.? mine is n * (number of prime numbers upto largest number )


feodorv:
20170623 02:00:27
I think it's my fault in misunderstanding the problem))) I was bound to guess that the solution must exist in any case. Meanwhile you could set one more problem (say ADACON0) with restricted rules for changing Ai ;) 

morass:
20170623 01:35:08
@feodorv: Even though it you passed a few testcases :P Anyway sorry for unclear statement :/ 

feodorv:
20170623 01:29:46
Oh, so i am solving other problem)))


morass:
20170623 01:13:39
@feodorv: Oh yes, you can forge a number any number of times ^_^ I'll try to update statement to make it more clear :P 

feodorv:
20170623 01:11:09
So we can change Ai to Ai+1 and then to Ai+2 and so on? 

morass:
20170623 00:33:29
@feodorv: Hello, for N==1, the answer is "the only element element" and gcd of two zero elements yield zero (according to mine definition). Thanks for asking ^_^ 

feodorv:
20170622 23:29:54
What should we do if there are two zero elements in the number list?)

Added by:  Morass 
Date:  20170622 
Time limit:  2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 