King George has recently decided that he would like to have a new
design for the royal graveyard. The graveyard must consist of several
sections, each of which must be a square of graves. All sections
must have different number of graves.

After a consultation with his astrologer, King George decided that
the lengths of section sides must be a sequence of successive
positive integer numbers. A section with side length s contains s^{2}
graves.

George has estimated the total number of graves
that will be located on the graveyard and now wants to know all
possible graveyard designs satisfying the condition.
You were asked to find them.

The picture below illustrates the graveyard for the first example.

Input file format

Input file contains n — the number of graves to be located in the graveyard.

Output file format

On the first line of the output file print k — the number of possible
graveyard designs. Next k lines must contain the descriptions of the
graveyards. Each line must start with l — the number of sections in the
corresponding graveyard, followed by l integers — the lengths of section
sides (successive positive integer numbers).

Change: sections must me enumerated in descending order.