from __future__ import annotations

from typing import Any





def     UpperCAmelCase						(   *lowercase							):







				"""simple docstring"""



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





def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



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





def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



				return [[x * n for x in row] for row in matrix]





def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



				if _check_not_integer(lowercase							) and _check_not_integer(lowercase							):
								__lowercase      ,					__lowercase			      =							_verify_matrix_sizes(lowercase							,      lowercase							)

				if cols[0] != rows[1]:
								__lowercase			      =							(
								    '''Cannot multiply matrix of dimensions '''
								    F"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
								)
								raise ValueError(lowercase							)
				return [
				    [sum(m * n for m, n in zip(lowercase							,      lowercase							)							) for j in zip(*lowercase							)] for i in matrix_a
				]





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							int(lowercase							)
				return [[int(row == column							) for column in range(lowercase							)] for row in range(lowercase							)]





def     UpperCAmelCase						(   lowercase							,      lowercase = True							):







				"""simple docstring"""



				if _check_not_integer(lowercase							):
								if return_map:
												return map(lowercase							,      zip(*lowercase							)							)
								else:
												return list(map(lowercase							,      zip(*lowercase							)							)							)
				raise TypeError('''Expected a matrix, got int/list instead'''							)





def     UpperCAmelCase						(   lowercase							,      lowercase							,      lowercase							):







				"""simple docstring"""



				__lowercase			      =							matrix[:row] + matrix[row + 1 :]
				return [row[:column] + row[column + 1 :] for row in minor]





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



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

				return sum(
				    x * determinant(minor(lowercase							,      0							,      lowercase							)							) * (-1) ** i
				    for i, x in enumerate(matrix[0]							)							)





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				__lowercase			      =							determinant(lowercase							)
				if det == 0:
								return None

				__lowercase			      =							[
				    [determinant(minor(lowercase							,      lowercase							,      lowercase							)							) for j in range(len(lowercase							)							)]
				    for i in range(len(lowercase							)							)
				]

				__lowercase			      =							[
				    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]							)]
				    for row in range(len(lowercase							)							)
				]
				__lowercase			      =							list(transpose(lowercase							)							)
				return scalar_multiply(lowercase							,      1 / det							)





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				return not isinstance(lowercase							,      lowercase							) and not isinstance(matrix[0]							,      lowercase							)





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				return len(lowercase							), len(matrix[0]							)





def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



				__lowercase			      =							_shape(lowercase							) + _shape(lowercase							)
				if shape[0] != shape[3] or shape[1] != shape[2]:
								__lowercase			      =							(
								    '''operands could not be broadcast together with shape '''
								    F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
								)
								raise ValueError(lowercase							)
				return (shape[0], shape[2]), (shape[1], shape[3])





def     UpperCAmelCase						(   ):







				"""simple docstring"""



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


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()
__a  :					Union[str, Any]          =  [[0, 1, 1], [0, 0, 1], [1, 0, 0]]




class        _UpperCamelCase				:


			"""simple docstring"""






			def __init__(       self				,       lowerCAmelCase__						)					-> List[str]:

							'''simple docstring'''


							__lowercase			      =							name
							__lowercase			      =							[]
							__lowercase			      =							[]





			def 	_SCREAMING_SNAKE_CASE      (       self				,       lowerCAmelCase__						)					-> Union[str, Any]:

							'''simple docstring'''


							self.inbound.append(lowerCAmelCase__						)





			def 	_SCREAMING_SNAKE_CASE      (       self				,       lowerCAmelCase__						)					-> Union[str, Any]:

							'''simple docstring'''


							self.outbound.append(lowerCAmelCase__						)





			def __repr__(       self						)					-> Tuple:

							'''simple docstring'''


							return F"<node={self.name} inbound={self.inbound} outbound={self.outbound}>"





def     UpperCAmelCase						(   lowercase							,      lowercase=3							,      lowercase=0.85							):







				"""simple docstring"""



				__lowercase			      =							{}
				for node in nodes:
								__lowercase			      =							1

				__lowercase			      =							{}
				for node in nodes:
								__lowercase			      =							len(node.outbound							)

				for i in range(lowercase							):
								print(F"======= Iteration {i + 1} ======="							)
								for _, node in enumerate(lowercase							):
												__lowercase			      =							(1 - d) + d * sum(
												    ranks[ib] / outbounds[ib] for ib in node.inbound							)
								print(lowercase							)





def     UpperCAmelCase						(   ):







				"""simple docstring"""



				__lowercase			      =							list(input('''Enter Names of the Nodes: '''							).split()							)

				__lowercase			      =							[Node(lowercase							) for name in names]

				for ri, row in enumerate(lowercase							):
								for ci, col in enumerate(lowercase							):
												if col == 1:
																nodes[ci].add_inbound(names[ri]							)
																nodes[ri].add_outbound(names[ci]							)

				print('''======= Nodes ======='''							)
				for node in nodes:
								print(lowercase							)

				page_rank(lowercase							)


if __name__ == "__main__":
		main()