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 so they would have their GCD greater than 1 ( gcd(a1,a2,a3,...,aN)>1). Anyway it is not easy to change a number - the only thing they can do is to go to a professor in mathematics, which could forge a number A into number A+1 or A-1. 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*105, the number of friend who were on trip (and also the number of numbers).

The second line contains N integers 0 ≤ ai ≤ 106

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

Added by:Morass
Date:2017-06-22
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All

hide comments
2017-06-23 01:11:09
So we can change Ai to Ai+1 and then to Ai+2 and so on?
2017-06-23 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 ^_^
2017-06-22 23:29:54
What should we do if there are two zero elements in the number list?)
Or N == 1?

Last edit: 2017-06-23 00:01:20
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