Ordered Fractions

Consider the set of all reduced fractions between 0 and 1 inclusive with denominators less than or equal to N.

Here is the set when N = 5:

Write a program that, given an integer N between 1 and 160 inclusive, prints the fractions in order of increasing magnitude.

Input

One line with a single integer N.

Output

One fraction per line, sorted in order of magnitude.

Examples