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.




var n = 20
say gather {
    for x in (1 .. n) {
        for y in (x .. n) {
           for z in (y .. n) {
             take([x,y,z]) if (x*x + y*y == z*z)
           }
        }
    }
}