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Problems

Ordered Fractions

Ordered Fractions

Time limit 1 second
Memory limit 64 MiB

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 data

One line with a single integer N.

Output data

One fraction per line, sorted in order of magnitude.

Examples

Input example #1
5
Output example #1
0/1
1/5
1/4
1/3
2/5
1/2
3/5
2/3
3/4
4/5
1/1