A list comprehension is a special syntax in some programming languages to describe lists. It is similar to the way mathematicians describe sets, with a set comprehension, hence the name.

Some attributes of a list comprehension are:

 They should be distinct from (nested) for loops and the use of map and filter functions within the syntax of the language.
 They should return either a list or an iterator (something that returns successive members of a collection, in order).
 The syntax has parts corresponding to that of set-builder notation. 


Task

Write a list comprehension that builds the list of all Pythagorean triples with elements between   1   and   n.

If the language has multiple ways for expressing such a construct (for example, direct list comprehensions and generators), write one example for each.




// version 1.0.6
 
fun pythagoreanTriples(n: Int) = 
    (1..n).flatMap { 
        x -> (x..n).flatMap { 
            y -> (y..n).filter {
                z ->  x * x + y * y == z * z 
            }.map { Triple(x, y, it) } 
        }
    }
 
fun main(args: Array<String>) {
    println(pythagoreanTriples(20))
}