sum-up-5

Plus and Minus were two little brothers who always fought over the N number of little cars they together owned.They usually begin counting in different groups of numbers but ultimately end up with the wrong total value.Exhausted at their failure they asked you for help.You must explain it to them that no matter how N is partitioned, the total value when summed up will always remain equal to N.
A partition of N is a way to write N as a sum of positive integers.The boys should understand that two sums are considered to be the same if they only differ in the order of their constituent summands. 

CONSTRAINTS: 1 ≤ N ≤ 22

INPUT
The first line contains the input N which is a positive integer value.

OUTPUT
 - First line displays the Total value i.e N
 - Each Consecutive line displays one of  all the possible methods of partition.

NOTE: Display the partitions in a proper order; from top to bottom, the numbers  present in each line either remain same or increase, in the end leaving us with  just 1s. Also take into consideration the fact that the partition of a number say 3 into "3 1 "  is same as " 1 3 "& hence the latter display summand should be discarded.

SAMPLE INPUT
Sample Input
4

SAMPLE OUTPUT
Sample Output
4
3 1
2 2
2 1 1
1 1 1 1

Explanation

NOTE: Display the partitions in a proper order; from top to bottom, the numbers  present in each line either remain same or increase, in the end leaving us with  just 1s. Also take into consideration the fact that the partition of a number say 3 into "3 1 "  is same as " 1 3 "& hence the latter display summand should be discarded.

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions: