SP32029 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 **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)

The first line contains an integer **1 , the number of friend who were on trip (and also the number of numbers).** The second line contains **N** integers 0

Print a single line with minimum number of operations to make a connection between all numbers.