If answer too big...clarification here
Problem ambiguous but finally solve! I scratched head for longest time, so clarification here to help others
Do not worry, no answer writed, only clarification:
IMPORTANT 1: One step = one grid COLUMN. Example show 2 steps:
*
**
Example show 2 steps:
*
**
**
Example show 4 steps:
*
*
*
**
***
****
IMPORTANT 2: Step HEIGHT > before step height. Example show all VALID N = 7:
VALID Staircase #1 of 4
*
*
*
*
*
**
VALID Staircase #2 of 4
*
*
*
**
**
VALID Staircase #3 of 4
*
**
**
**
VALID Staircase #4 of 4
*
*
**
***
Example of INVALID N = 7:
INVALID Staircase:
*
*
*
*
*
*
*
Invalid because only 1 step
INVALID Staircase:
*
***
***
Invalid because 2 steps same height (height 2, height 2, height 3)
INVALID Staircase:
* *
* *
***
Invalid because step height not > before step (height 3, height 1, height 3)