sir

As we well know, Gigel likes to play with numbers. While playing he has noticed that some sequences of numbers have peculiar properties. For example: he has noticed that positive integer sequence 1, 3, 5 has the following properties:
- it is ascending
- 1>=1; 1+3>=22; 1+3+5>=32
- 1+3+5=32
While on the other hand, sequence 1, 2, 6 doesn't have all these properties because the sum of its first two elements is less than 4. Generalizing, Gigel has named these sequences special sequences. So, the sequence a1, a2, .., an of positive integers is called a special sequence of rank n if it meets the following conditions:

  1. a1+a2+ ... +ak>=k2 (for any k >= 1)
  2. a1+ ... +an=n2
  3. a1<=a2<= ... <=an

Task
Gigel would like you to write a program that generates special sequences of a given rank.

Input Data
Input file sir.in will contain a single line with a positive integer n which is the rank of the special sequences that will be generated.

Output Data
Output file sir.out contains on each line a special sequence of rank n. Each sequences is written on one line, with its elements separated by a space. The sequences are going to be generated in lexico-graphical order. If the total number of sequences that will have to be written is more than 40 they won't all be written; only the first 20 and afterwards the last 20 will be written.

Restrictions
1<=n<=30

Examples
sir.in
sir.out sir.in sir.out
3 1 3 5
1 4 4
2 2 5
2 3 4
3 3 3
5 1 3 5 7 9
1 3 5 8 8
1 3 6 6 9
1 3 6 7 8
1 3 7 7 7
1 4 4 7 9
1 4 4 8 8
1 4 5 6 9
1 4 5 7 8
1 4 6 6 8
1 4 6 7 7
1 5 5 5 9
1 5 5 6 8
1 5 5 7 7
1 5 6 6 7
1 6 6 6 6
2 2 5 7 9
2 2 5 8 8
2 2 6 6 9
2 2 6 7 8
3 3 4 7 8
3 3 5 5 9
3 3 5 6 8
3 3 5 7 7
3 3 6 6 7
3 4 4 5 9
3 4 4 6 8
3 4 4 7 7
3 4 5 5 8
3 4 5 6 7
3 4 6 6 6
3 5 5 5 7
3 5 5 6 6
4 4 4 4 9
4 4 4 5 8
4 4 4 6 7
4 4 5 5 7
4 4 5 6 6
4 5 5 5 6
5 5 5 5 5

Time limit: 0.1 seconds

Marinel Serban
"Gr. C. Moisil" Iaşi IT High School
marinel_serban@yahoo.com