



'''simple docstring'''





def lowerCAmelCase  ():



     """simple docstring"""



     return [list(range(1_000 - i  ,	-1_000 - i  ,	-1)) for i in range(1_000)]


lowercase_		       =  generate_large_matrix()
lowercase_		       =  (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)




def lowerCAmelCase  (__A):



     """simple docstring"""



     assert all(row == sorted(__A  ,	reverse=__A) for row in grid)
     assert all(list(__A) == sorted(__A  ,	reverse=__A) for col in zip(*__A))




def lowerCAmelCase  (__A):



     """simple docstring"""



     _a      =  0
     _a      =  len(__A) - 1

     # Edge cases such as no values or all numbers are negative.
     if not array or array[0] < 0:
          return 0

     while right + 1 > left:
          _a      =  (left + right) // 2
          _a      =  array[mid]

          # Num must be negative and the index must be greater than or equal to 0.
          if num < 0 and array[mid - 1] >= 0:
               return mid

          if num >= 0:
               _a      =  mid + 1
          else:
               _a      =  mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
     return len(__A)




def lowerCAmelCase  (__A):



     """simple docstring"""



     _a      =  0
     _a      =  len(grid[0])

     for i in range(len(__A)):
          _a      =  find_negative_index(grid[i][:bound])
          total += bound
     return (len(__A) * len(grid[0])) - total




def lowerCAmelCase  (__A):



     """simple docstring"""



     return len([number for row in grid for number in row if number < 0])




def lowerCAmelCase  (__A):



     """simple docstring"""



     _a      =  0
     for row in grid:
          for i, number in enumerate(__A):
               if number < 0:
                    total += len(__A) - i
                    break
     return total




def lowerCAmelCase  ():



     """simple docstring"""



     from timeit import timeit

     print('''Running benchmarks''')
     _a      =  (
         '''from __main__ import count_negatives_binary_search, '''
         '''count_negatives_brute_force, count_negatives_brute_force_with_break, grid'''
     )
     for func in (
         "count_negatives_binary_search",  # took 0.7727 seconds
         "count_negatives_brute_force_with_break",  # took 4.6505 seconds
         "count_negatives_brute_force",  # took 12.8160 seconds
     ):
          _a      =  timeit(F'''{func}(grid=grid)'''  ,	setup=__A  ,	number=500)
          print(F'''{func}() took {time:0.4f} seconds''')


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()








'''simple docstring'''





from __future__ import annotations

from typing import TypedDict






class __A			(  A						):



 '''simple docstring'''







 __lowerCamelCase    :       str
 __lowerCamelCase    :       int





def lowerCAmelCase  (__A):



     """simple docstring"""



     if not isinstance(__A  ,	__A):
          raise TypeError('''The parameter s type must be str.''')

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




def lowerCAmelCase  (__A):



     """simple docstring"""



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

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




def lowerCAmelCase  (__A  ,	__A):



     """simple docstring"""



     if not isinstance(__A  ,	__A):
          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:
          _a      =  int(__A)
     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(__A):
          raise ValueError(
              '''The parameter idx_original_string must be lower than''' ''' len(bwt_string).''')

     _a      =  [''''''] * len(__A)
     for _ in range(len(__A)):
          for i in range(len(__A)):
               _a      =  bwt_string[i] + ordered_rotations[i]
          ordered_rotations.sort()
     return ordered_rotations[idx_original_string]


if __name__ == "__main__":
  lowercase_		       =  "Provide a string that I will generate its BWT transform: "
  lowercase_		       =  input(entry_msg).strip()
  lowercase_		       =  bwt_transform(s)
  print(
      F"""Burrows Wheeler transform for string '{s}' results """
      F"""in '{result['bwt_string']}'"""
  )
  lowercase_		       =  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}'"""
  )



