




"""simple docstring"""



from __future__ import annotations

import math







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		list:
 if len(lowercase_						) != 2 or len(a[0]						) != 2 or len(lowercase_						) != 2 or len(b[0]						) != 2:
  raise Exception("Matrices are not 2x2"						)
 A__	=    [
     [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
     [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
 ]
 return new_matrix







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		Optional[Any]:
 return [
     [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
     for row in range(len(lowercase_						)						)
 ]







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		str:
 return [
     [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
     for row in range(len(lowercase_						)						)
 ]







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		tuple[list, list, list, list]:
 if len(lowercase_						) % 2 != 0 or len(a[0]						) % 2 != 0:
  raise Exception("Odd matrices are not supported!"						)

 A__	=    len(lowercase_						)
 A__	=    matrix_length // 2

 A__	=    [[a[i][j] for j in range(lowercase_      ,			lowercase_						)] for i in range(lowercase_						)]
 A__	=    [
     [a[i][j] for j in range(lowercase_      ,			lowercase_						)] for i in range(lowercase_      ,			lowercase_						)
 ]

 A__	=    [[a[i][j] for j in range(lowercase_						)] for i in range(lowercase_						)]
 A__	=    [[a[i][j] for j in range(lowercase_						)] for i in range(lowercase_      ,			lowercase_						)]

 return top_left, top_right, bot_left, bot_right







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		tuple[int, int]:
 return len(lowercase_						), len(matrix[0]						)







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		None:
 print("\n".join(str(lowercase_						) for line in matrix						)						)







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		list:
 if matrix_dimensions(lowercase_						) == (2, 2):
  return default_matrix_multiplication(lowercase_      ,			lowercase_						)

 A__,				A__,				A__,				A__	=    split_matrix(lowercase_						)
 A__,				A__,				A__,				A__	=    split_matrix(lowercase_						)

 A__	=    actual_strassen(lowercase_      ,			matrix_subtraction(lowercase_      ,			lowercase_						)						)
 A__	=    actual_strassen(matrix_addition(lowercase_      ,			lowercase_						)      ,			lowercase_						)
 A__	=    actual_strassen(matrix_addition(lowercase_      ,			lowercase_						)      ,			lowercase_						)
 A__	=    actual_strassen(lowercase_      ,			matrix_subtraction(lowercase_      ,			lowercase_						)						)
 A__	=    actual_strassen(matrix_addition(lowercase_      ,			lowercase_						)      ,			matrix_addition(lowercase_      ,			lowercase_						)						)
 A__	=    actual_strassen(matrix_subtraction(lowercase_      ,			lowercase_						)      ,			matrix_addition(lowercase_      ,			lowercase_						)						)
 A__	=    actual_strassen(matrix_subtraction(lowercase_      ,			lowercase_						)      ,			matrix_addition(lowercase_      ,			lowercase_						)						)

 A__	=    matrix_addition(matrix_subtraction(matrix_addition(lowercase_      ,			lowercase_						)      ,			lowercase_						)      ,			lowercase_						)
 A__	=    matrix_addition(lowercase_      ,			lowercase_						)
 A__	=    matrix_addition(lowercase_      ,			lowercase_						)
 A__	=    matrix_subtraction(matrix_subtraction(matrix_addition(lowercase_      ,			lowercase_						)      ,			lowercase_						)      ,			lowercase_						)

 # construct the new matrix from our 4 quadrants
 A__	=    []
 for i in range(len(lowercase_						)						):
  new_matrix.append(top_left[i] + top_right[i]						)
 for i in range(len(lowercase_						)						):
  new_matrix.append(bot_left[i] + bot_right[i]						)
 return new_matrix







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		list:
 if matrix_dimensions(lowercase_						)[1] != matrix_dimensions(lowercase_						)[0]:
  A__	=    (
      "Unable to multiply these matrices, please check the dimensions.\n"
      f"""Matrix A: {matrixa}\n"""
      f"""Matrix B: {matrixa}"""
  )
  raise Exception(lowercase_						)
 A__	=    matrix_dimensions(lowercase_						)
 A__	=    matrix_dimensions(lowercase_						)

 if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
  return [matrixa, matrixa]

 A__	=    max(*lowercase_      ,			*lowercase_						)
 A__	=    int(math.pow(2      ,			math.ceil(math.loga(lowercase_						)						)						)						)
 A__	=    matrixa
 A__	=    matrixa

 # Adding zeros to the matrices so that the arrays dimensions are the same and also
 # power of 2
 for i in range(0      ,			lowercase_						):
  if i < dimensiona[0]:
   for _ in range(dimensiona[1]      ,			lowercase_						):
    new_matrixa[i].append(0						)
  else:
   new_matrixa.append([0] * maxim						)
  if i < dimensiona[0]:
   for _ in range(dimensiona[1]      ,			lowercase_						):
    new_matrixa[i].append(0						)
  else:
   new_matrixa.append([0] * maxim						)

 A__	=    actual_strassen(lowercase_      ,			lowercase_						)

 # Removing the additional zeros
 for i in range(0      ,			lowercase_						):
  if i < dimensiona[0]:
   for _ in range(dimensiona[1]      ,			lowercase_						):
    final_matrix[i].pop()
  else:
   final_matrix.pop()
 return final_matrix


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE    =	[
          [2, 3, 4, 5],
          [6, 4, 3, 1],
          [2, 3, 6, 7],
          [3, 1, 2, 4],
          [2, 3, 4, 5],
          [6, 4, 3, 1],
          [2, 3, 6, 7],
          [3, 1, 2, 4],
          [2, 3, 4, 5],
          [6, 2, 3, 1],
      ]
      SCREAMING_SNAKE_CASE    =	[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
      print(strassen(matrixa, matrixa))











"""simple docstring"""



from __future__ import annotations

SCREAMING_SNAKE_CASE    =	"#"




class      UpperCAmelCase_  :




    def __init__(   self						:	Dict				)				->							None:




     '''simple docstring'''

     A__	=    {}




    def 							__magic_name__							(   self						:	Optional[Any]     ,			snake_case_						:	str				)				->							None:




     '''simple docstring'''

     A__	=    self._trie
     for char in text:
      if char not in trie:
       A__	=    {}
      A__	=    trie[char]
     A__	=    True




    def 							__magic_name__							(   self						:	List[Any]     ,			snake_case_						:	str				)				->							tuple | list:




     '''simple docstring'''

     A__	=    self._trie
     for char in prefix:
      if char in trie:
       A__	=    trie[char]
      else:
       return []
     return self._elements(snake_case_				)




    def 							__magic_name__							(   self						:	Union[str, Any]     ,			snake_case_						:	dict				)				->							tuple:




     '''simple docstring'''

     A__	=    []
     for c, v in d.items():
      A__	=    [" "] if c == END else [(c + s) for s in self._elements(snake_case_				)]
      result.extend(snake_case_				)
     return tuple(snake_case_				)






SCREAMING_SNAKE_CASE    =	Trie()
SCREAMING_SNAKE_CASE    =	("depart", "detergent", "daring", "dog", "deer", "deal")
for word in words:
      trie.insert_word(word)







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		tuple:
 A__	=    trie.find_word(lowercase_						)
 return tuple(string + word for word in suffixes						)







def   _SCREAMING_SNAKE_CASE       (							)						->		None:
 print(autocomplete_using_trie("de"						)						)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()





