Farey fractions of level one are defined as sequence ( , ). This sequence is extended in level two to form a sequence (  ,  ,  ), sequence (  ,  , ,  , ) at level three, sequence (   , ,   ,  ,  , , )...

Farey fractions of level one are defined as sequence (
,
). This sequence is extended in level two to

form a sequence ( , , ), sequence ( , ,, ,) at level three, sequence (  ,,
  ,
 ,
 ,
,
) at level four, so that at each level
, a new fraction
is inserted between two neighbor fractions
and
 only if

. Write a program which for a number
 entered by the user creates—by constantly extending it—a linked list of fractions at level and then displays them.