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.




typealias F1 = (Int) -> [(Int, Int, Int)]
typealias F2 = (Int) -> Bool
 
func pythagoreanTriples(n: Int) -> [(Int, Int, Int)] {
  (1...n).flatMap({x in
    (x...n).flatMap({y in
      (y...n).filter({z in
        x * x + y * y == z * z
      } as F2).map({ (x, y, $0) })
    } as F1)
  } as F1)
}
 
print(pythagoreanTriples(n: 20))