From Wikipedia, the free encyclopedia:

 A happy number is defined by the following process:
 Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals   1   (where it will stay),   or it loops endlessly in a cycle which does not include   1.   


 Those numbers for which this process end in   1   are       happy   numbers,   
 while   those numbers   that   do   not   end in   1   are   unhappy   numbers. 


Task

Find and print the first   8   happy numbers.

Display an example of your output here on this page.



See also

   The OEIS entry:   The     happy numbers:   A007770
   The OEIS entry:   The unhappy numbers;   A031177


Number.metaClass.isHappy = {
    def number = delegate as Long
    def cycle = new HashSet<Long>()
    while (number != 1 && !cycle.contains(number)) {
        cycle << number
        number = (number as String).collect { d = (it as Long); d * d }.sum()
    }
    number == 1
}
 
def matches = []
for (int i = 0; matches.size() < 8; i++) {
    if (i.happy) { matches << i }
}
println matches