1

Break Number

Difficulty: MEDIUM
Contributed By
Avg. time to solve
35 min
Success Rate
70%

Problem Statement

Given a number 'N', you need to find all possible unique ways to represent this number as the sum of positive integers.

Note
1. By unique it is meant that no other composition can be expressed as a permutation of the generated composition. For eg. [1, 2, 1] and [1, 1, 2] are not unique.  

2. You need to print all combinations in non-decreasing order for eg. [1, 2, 1] or [1, 1, 2] will be printed as [1, 1, 2], however, the order of printing all the sequences can be random. 
Input Format:
The first and the only line of the input contains an integer 'N' representing the given number.
Output Format:
Each line of the output contains one unique sequence which sums up to 'N'.

There will be 'K' lines of output containing one unique sequence on each line in non-decreasing order which sums up to 'N'. 'K' is the total number of unique sequences. 
Note:
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints:
1 <= N <= 50

Time Limit: 1sec
Sample Input 1:
4
Sample Output 1:
4
1 1 1 1 
1 1 2
2 2
1 3
Explanation For Sample Input 1:
Here notice that all combinations are sorted in non-decreasing order and [1, 1, 2] and [1, 2, 1] are the same and printed as [1, 1, 2]. 

Note: 1 1 1 1
      2 2
      4 
      1 3
      1 1 2  is also a valid output as the order of different sequences doesn’t matter.
Sample Input 2:
1
Sample Output 2:
1
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