The Farey sequence of order n is the set of all fractions with a denominator between 1 and n (reduced to its lowest terms and ordered ascendingly). Given an n, write a function that returns the Farey sequence as an array with a string representation of each fraction of the form "numerator/denominator".

Examples

farey(1) ➞ ["0/1", "1/1"]

farey(5) ➞ ["0/1", "1/5", "1/4", "1/3", "2/5", "1/2", "3/5", "2/3", "3/4", "4/5", "1/1"]

farey(7) ➞ ["0/1", "1/7", "1/6", "1/5", "1/4", "2/7", "1/3", "2/5", "3/7", "1/2", "4/7", "3/5", "2/3", "5/7", "3/4", "4/5", "5/6", "6/7", "1/1"]

Notes

• The sequence should always start with "0/1" and end with "1/1".
• It is expected from the challenge-takers to come up with a solution using the concept of recursion or the so-called recursive approach.
• You can read on more topics about recursion (see Resources tab) if you aren't familiar with it yet or hasn't fully understood the concept behind it before taking up this challenge or unless otherwise.
• There will be no exceptions to handle, all inputs are positive integers.
• A recursive approach is prone to Uncaught RangeError or exceededing the maximum call size of the stack.
• Optional: Try to solve this with the least lines of code.
• If you think recursion is fun, you can find a collection of those challenges here.