The Farey sequence of order n is the set of all fractions with a denominator between 1 and n, reduced and returned in ascending order. Given n, return the Farey sequence as an array, with each fraction being represented by a string in the form "numerator/denominator".

Examples

farey(1) ➞ ["0/1", "1/1"]

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

Notes

The Farey sequence will always begin with "0/1" and end with "1/1".