'''simple docstring'''




from __future__ import annotations

from typing import TypedDict


class       UpperCAmelCase__  (       _snake_case			):






   """simple docstring"""
   A							:       str
   A							:       int


def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):
     if not isinstance(lowerCamelCase__  ,       lowerCamelCase__							):
          raise TypeError('The parameter s type must be str.'							)

     return [s[i:] + s[:i] for i in range(len(lowerCamelCase__							)							)]

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):
     if not isinstance(lowerCamelCase__  ,       lowerCamelCase__							):
          raise TypeError('The parameter s type must be str.'							)
     if not s:
          raise ValueError('The parameter s must not be empty.'							)

     lowercase_					:       Any     				=					all_rotations(lowerCamelCase__							)
     rotations.sort()  # sort the list of rotations in alphabetically order
     # make a string composed of the last char of each rotation
     lowercase_					:       List[str]     				=					{
         'bwt_string': ''.join([word[-1] for word in rotations]							),
         'idx_original_string': rotations.index(lowerCamelCase__							),
     }
     return response

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_  ,       SCREAMING_SNAKE_CASE_							):
     if not isinstance(lowerCamelCase__  ,       lowerCamelCase__							):
          raise TypeError('The parameter bwt_string type must be str.'							)
     if not bwt_string:
          raise ValueError('The parameter bwt_string must not be empty.'							)
     try:
          lowercase_					:       Tuple     				=					int(lowerCamelCase__							)
     except ValueError:
          raise TypeError(
              'The parameter idx_original_string type must be int or passive'
              ' of cast to int.'							)
     if idx_original_string < 0:
          raise ValueError('The parameter idx_original_string must not be lower than 0.'							)
     if idx_original_string >= len(lowerCamelCase__							):
          raise ValueError(
              'The parameter idx_original_string must be lower than' ' len(bwt_string).'							)

     lowercase_					:       Optional[Any]     				=					[''] * len(lowerCamelCase__							)
     for _ in range(len(lowerCamelCase__							)							):
          for i in range(len(lowerCamelCase__							)							):
               lowercase_					:       int     				=					bwt_string[i] + ordered_rotations[i]
          ordered_rotations.sort()
     return ordered_rotations[idx_original_string]


if __name__ == "__main__":
 _A								=   'Provide a string that I will generate its BWT transform: '
 _A								=   input(entry_msg).strip()
 _A								=   bwt_transform(s)
 print(
     F"""Burrows Wheeler transform for string \'{s}\' results """
     F"""in \'{result["bwt_string"]}\'"""
 )
 _A								=   reverse_bwt(result['bwt_string'], result['idx_original_string'])
 print(
     F"""Reversing Burrows Wheeler transform for entry \'{result["bwt_string"]}\' """
     F"""we get original string \'{original_string}\'"""
 )





'''simple docstring'''




from __future__ import annotations

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):

     # preprocessing the first row
     for i in range(1  ,       len(matrix[0]							)							):
          matrix[0][i] += matrix[0][i - 1]

     # preprocessing the first column
     for i in range(1  ,       len(SCREAMING_SNAKE_CASE_							)							):
          matrix[i][0] += matrix[i - 1][0]

     # updating the path cost for current position
     for i in range(1  ,       len(SCREAMING_SNAKE_CASE_							)							):
          for j in range(1  ,       len(matrix[0]							)							):
               matrix[i][j] += min(matrix[i - 1][j]  ,       matrix[i][j - 1]							)

     return matrix[-1][-1]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




