

"""simple docstring"""




from __future__ import annotations

from typing import Any
def 					lowerCAmelCase  (   *__UpperCamelCase ):
 '''simple docstring'''





 if all(_check_not_integer(__UpperCamelCase ) for m in matrix_s ):
  for i in matrix_s[1:]:
   _verify_matrix_sizes(matrix_s[0]							,      __UpperCamelCase )
  return [[sum(__UpperCamelCase ) for t in zip(*__UpperCamelCase )] for m in zip(*__UpperCamelCase )]
 raise TypeError("""Expected a matrix, got int/list instead""" )
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 if (
     _check_not_integer(__UpperCamelCase )
     and _check_not_integer(__UpperCamelCase )
     and _verify_matrix_sizes(__UpperCamelCase							,      __UpperCamelCase )
 ):
  return [[i - j for i, j in zip(*__UpperCamelCase )] for m in zip(__UpperCamelCase							,      __UpperCamelCase )]
 raise TypeError("""Expected a matrix, got int/list instead""" )
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 return [[x * n for x in row] for row in matrix]
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 if _check_not_integer(__UpperCamelCase ) and _check_not_integer(__UpperCamelCase ):
  UpperCAmelCase__				, UpperCAmelCase__   :					Union[str, Any]   				=   _verify_matrix_sizes(__UpperCamelCase							,      __UpperCamelCase )

 if cols[0] != rows[1]:
  UpperCAmelCase__   :					List[Any]   				=   (
      """Cannot multiply matrix of dimensions """
      F"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
  )
  raise ValueError(__UpperCamelCase )
 return [
     [sum(m * n for m, n in zip(__UpperCamelCase							,      __UpperCamelCase ) ) for j in zip(*__UpperCamelCase )] for i in matrix_a
 ]
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					Tuple   				=   int(__UpperCamelCase )
 return [[int(row == column ) for column in range(__UpperCamelCase )] for row in range(__UpperCamelCase )]
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase = True ):
 '''simple docstring'''





 if _check_not_integer(__UpperCamelCase ):
  if return_map:
   return map(__UpperCamelCase							,      zip(*__UpperCamelCase ) )
  else:
   return list(map(__UpperCamelCase							,      zip(*__UpperCamelCase ) ) )
 raise TypeError("""Expected a matrix, got int/list instead""" )
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					List[str]   				=   matrix[:row] + matrix[row + 1 :]
 return [row[:column] + row[column + 1 :] for row in minor]
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 if len(__UpperCamelCase ) == 1:
  return matrix[0][0]

 return sum(
     x * determinant(minor(__UpperCamelCase							,      0							,      __UpperCamelCase ) ) * (-1) ** i
     for i, x in enumerate(matrix[0] ) )
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					int   				=   determinant(__UpperCamelCase )
 if det == 0:
  return None

 UpperCAmelCase__   :					List[str]   				=   [
     [determinant(minor(__UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase ) ) for j in range(len(__UpperCamelCase ) )]
     for i in range(len(__UpperCamelCase ) )
 ]

 UpperCAmelCase__   :					Any   				=   [
     [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row] )]
     for row in range(len(__UpperCamelCase ) )
 ]
 UpperCAmelCase__   :					str   				=   list(transpose(__UpperCamelCase ) )
 return scalar_multiply(__UpperCamelCase							,      1 / det )
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 return not isinstance(__UpperCamelCase							,      __UpperCamelCase ) and not isinstance(matrix[0]							,      __UpperCamelCase )
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 return len(__UpperCamelCase ), len(matrix[0] )
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					Dict   				=   _shape(__UpperCamelCase ) + _shape(__UpperCamelCase )
 if shape[0] != shape[3] or shape[1] != shape[2]:
  UpperCAmelCase__   :					List[str]   				=   (
      """operands could not be broadcast together with shape """
      F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
  )
  raise ValueError(__UpperCamelCase )
 return (shape[0], shape[2]), (shape[1], shape[3])
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 UpperCAmelCase__   :					Any   				=   [[12, 10], [3, 9]]
 UpperCAmelCase__   :					Optional[Any]   				=   [[3, 4], [7, 4]]
 UpperCAmelCase__   :					List[Any]   				=   [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
 UpperCAmelCase__   :					str   				=   [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
 print(F"Add Operation, {add(__UpperCamelCase							,      __UpperCamelCase ) = } \n" )
 print(
     F"Multiply Operation, {multiply(__UpperCamelCase							,      __UpperCamelCase ) = } \n"							,      )
 print(F"Identity: {identity(5 )}\n" )
 print(F"Minor of {matrix_c} = {minor(__UpperCamelCase							,      1							,      2 )} \n" )
 print(F"Determinant of {matrix_b} = {determinant(__UpperCamelCase )} \n" )
 print(F"Inverse of {matrix_d} = {inverse(__UpperCamelCase )}\n" )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()








"""simple docstring"""




from __future__ import annotations
def 					lowerCAmelCase  (   __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__				, UpperCAmelCase__   :					Optional[Any]   				=   m - 1, 0
 while i >= 0 and j < n:
  if key == mat[i][j]:
   print(F"Key {key} found at row- {i + 1} column- {j + 1}" )
   return
  if key < mat[i][j]:
   i -= 1
  else:
   j += 1
 print(F"Key {key} not found" )
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 UpperCAmelCase__   :					Union[str, Any]   				=   [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]]
 UpperCAmelCase__   :					int   				=   int(input("""Enter the element to be searched:""" ) )
 print(__UpperCamelCase )
 search_in_a_sorted_matrix(__UpperCamelCase							,      len(__UpperCamelCase )							,      len(mat[0] )							,      __UpperCamelCase )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()





