




from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload

class 		__lowerCAmelCase	:
							def __init__(						self						:List[str]		,      __magic_name__						:Collection[float] | None = None				):







								'''simple docstring'''







								if components is None:
									a										=							[]
								a										=							list(__magic_name__				)
							def __len__(						self						:str				):







								'''simple docstring'''







								return len(self.__components				)
							def __str__(						self						:Union[str, Any]				):







								'''simple docstring'''







								return "(" + ",".join(map(__magic_name__		,      self.__components				)				) + ")"
							def __add__(						self						:int		,      __magic_name__						:Vector				):







								'''simple docstring'''







								a										=							len(self				)
								if size == len(__magic_name__				):
									a										=							[self.__components[i] + other.component(__magic_name__				) for i in range(__magic_name__				)]
									return Vector(__magic_name__				)
								else:
									raise Exception("""must have the same size"""				)
							def __sub__(						self						:Dict		,      __magic_name__						:Vector				):







								'''simple docstring'''







								a										=							len(self				)
								if size == len(__magic_name__				):
									a										=							[self.__components[i] - other.component(__magic_name__				) for i in range(__magic_name__				)]
									return Vector(__magic_name__				)
								else:  # error case
									raise Exception("""must have the same size"""				)
							@overload
							def __mul__(						self						:Optional[int]		,      __magic_name__						:float				):







								'''simple docstring'''







								...
							@overload
							def __mul__(						self						:Optional[Any]		,      __magic_name__						:Vector				):







								'''simple docstring'''







								...
							def __mul__(						self						:int		,      __magic_name__						:float | Vector				):







								'''simple docstring'''







								if isinstance(__magic_name__		,      (float, int)				):
									a										=							[c * other for c in self.__components]
									return Vector(__magic_name__				)
								elif isinstance(__magic_name__		,      __magic_name__				) and len(self				) == len(__magic_name__				):
									a										=							len(self				)
									a										=							[self.__components[i] * other.component(__magic_name__				) for i in range(__magic_name__				)]
									return sum(__magic_name__				)
								else:  # error case
									raise Exception("""invalid operand!"""				)
							def       lowerCamelCase__							(						self						:Tuple				):







								'''simple docstring'''







								return Vector(self.__components				)
							def       lowerCamelCase__							(						self						:Tuple		,      __magic_name__						:int				):







								'''simple docstring'''







								if isinstance(__magic_name__		,      __magic_name__				) and -len(self.__components				) <= i < len(self.__components				):
									return self.__components[i]
								else:
									raise Exception("""index out of range"""				)
							def       lowerCamelCase__							(						self						:str		,      __magic_name__						:int		,      __magic_name__						:float				):







								'''simple docstring'''







								assert -len(self.__components				) <= pos < len(self.__components				)
								a										=							value
							def       lowerCamelCase__							(						self						:Union[str, Any]				):







								'''simple docstring'''







								if len(self.__components				) == 0:
									raise Exception("""Vector is empty"""				)
								a										=							[c**2 for c in self.__components]
								return math.sqrt(sum(__magic_name__				)				)





							def       lowerCamelCase__							(						self						:int		,      __magic_name__						:Vector		,      __magic_name__						:bool = False				):







								'''simple docstring'''







								a										=							self * other
								a										=							self.euclidean_length() * other.euclidean_length()
								if deg:
									return math.degrees(math.acos(num / den				)				)
								else:
									return math.acos(num / den				)







def 		__A		(	__lowerCamelCase    )      ->       Vector:
	assert isinstance(__lowerCamelCase							,			__lowerCamelCase    )
	return Vector([0] * dimension    )





def 		__A		(	__lowerCamelCase							,			__lowerCamelCase    )      ->       Vector:
	assert isinstance(__lowerCamelCase							,			__lowerCamelCase    ) and (isinstance(__lowerCamelCase							,			__lowerCamelCase    ))
	a										=							[0] * dimension
	a										=							1
	return Vector(__lowerCamelCase    )





def 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )      ->       Vector:
	assert (
	    isinstance(__lowerCamelCase							,			__lowerCamelCase    )
	    and isinstance(__lowerCamelCase							,			__lowerCamelCase    )
	    and (isinstance(__lowerCamelCase							,			(int, float)    ))
	)
	return x * scalar + y





def 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )      ->       Vector:
	random.seed(__lowerCamelCase    )
	a										=							[random.randint(__lowerCamelCase							,			__lowerCamelCase    ) for _ in range(__lowerCamelCase    )]
	return Vector(__lowerCamelCase    )

class 		__lowerCAmelCase	:
							def __init__(						self						:Dict		,      __magic_name__						:list[list[float]]		,      __magic_name__						:int		,      __magic_name__						:int				):







								'''simple docstring'''







								a										=							matrix
								a										=							w
								a										=							h
							def __str__(						self						:Dict				):







								'''simple docstring'''







								a										=							""""""
								for i in range(self.__height				):
									ans += "|"
									for j in range(self.__width				):
										if j < self.__width - 1:
											ans += str(self.__matrix[i][j]				) + ","
										else:
											ans += str(self.__matrix[i][j]				) + "|\n"
								return ans
							def __add__(						self						:Optional[Any]		,      __magic_name__						:Matrix				):







								'''simple docstring'''







								if self.__width == other.width() and self.__height == other.height():
									a										=							[]
									for i in range(self.__height				):
										a										=							[
										    self.__matrix[i][j] + other.component(__magic_name__		,      __magic_name__				)
										    for j in range(self.__width				)
										]
										matrix.append(__magic_name__				)
									return Matrix(__magic_name__		,      self.__width		,      self.__height				)
								else:
									raise Exception("""matrix must have the same dimension!"""				)
							def __sub__(						self						:List[str]		,      __magic_name__						:Matrix				):







								'''simple docstring'''







								if self.__width == other.width() and self.__height == other.height():
									a										=							[]
									for i in range(self.__height				):
										a										=							[
										    self.__matrix[i][j] - other.component(__magic_name__		,      __magic_name__				)
										    for j in range(self.__width				)
										]
										matrix.append(__magic_name__				)
									return Matrix(__magic_name__		,      self.__width		,      self.__height				)
								else:
									raise Exception("""matrices must have the same dimension!"""				)
							@overload
							def __mul__(						self						:List[str]		,      __magic_name__						:float				):







								'''simple docstring'''







								...
							@overload
							def __mul__(						self						:Union[str, Any]		,      __magic_name__						:Vector				):







								'''simple docstring'''







								...
							def __mul__(						self						:Any		,      __magic_name__						:float | Vector				):







								'''simple docstring'''







								if isinstance(__magic_name__		,      __magic_name__				):  # matrix-vector
									if len(__magic_name__				) == self.__width:
										a										=							zero_vector(self.__height				)
										for i in range(self.__height				):
											a										=							[
											    self.__matrix[i][j] * other.component(__magic_name__				)
											    for j in range(self.__width				)
											]
											ans.change_component(__magic_name__		,      sum(__magic_name__				)				)
										return ans
									else:
										raise Exception(
										    """vector must have the same size as the """
										    """number of columns of the matrix!"""				)
								elif isinstance(__magic_name__		,      (int, float)				):  # matrix-scalar
									a										=							[
									    [self.__matrix[i][j] * other for j in range(self.__width				)]
									    for i in range(self.__height				)
									]
									return Matrix(__magic_name__		,      self.__width		,      self.__height				)
								return None
							def       lowerCamelCase__							(						self						:str				):







								'''simple docstring'''







								return self.__height
							def       lowerCamelCase__							(						self						:int				):







								'''simple docstring'''







								return self.__width
							def       lowerCamelCase__							(						self						:int		,      __magic_name__						:int		,      __magic_name__						:int				):







								'''simple docstring'''







								if 0 <= x < self.__height and 0 <= y < self.__width:
									return self.__matrix[x][y]
								else:
									raise Exception("""change_component: indices out of bounds"""				)
							def       lowerCamelCase__							(						self						:Dict		,      __magic_name__						:int		,      __magic_name__						:int		,      __magic_name__						:float				):







								'''simple docstring'''







								if 0 <= x < self.__height and 0 <= y < self.__width:
									a										=							value
								else:
									raise Exception("""change_component: indices out of bounds"""				)
							def       lowerCamelCase__							(						self						:Tuple		,      __magic_name__						:int		,      __magic_name__						:int				):







								'''simple docstring'''







								if self.__height != self.__width:
									raise Exception("""Matrix is not square"""				)
								a										=							self.__matrix[:x] + self.__matrix[x + 1 :]
								for i in range(len(__magic_name__				)				):
									a										=							minor[i][:y] + minor[i][y + 1 :]
								return Matrix(__magic_name__		,      self.__width - 1		,      self.__height - 1				).determinant()
							def       lowerCamelCase__							(						self						:Tuple		,      __magic_name__						:int		,      __magic_name__						:int				):







								'''simple docstring'''







								if self.__height != self.__width:
									raise Exception("""Matrix is not square"""				)
								if 0 <= x < self.__height and 0 <= y < self.__width:
									return (-1) ** (x + y) * self.minor(__magic_name__		,      __magic_name__				)
								else:
									raise Exception("""Indices out of bounds"""				)





							def       lowerCamelCase__							(						self						:List[str]				):







								'''simple docstring'''







								if self.__height != self.__width:
									raise Exception("""Matrix is not square"""				)
								if self.__height < 1:
									raise Exception("""Matrix has no element"""				)
								elif self.__height == 1:
									return self.__matrix[0][0]
								elif self.__height == 2:
									return (
									    self.__matrix[0][0] * self.__matrix[1][1]
									    - self.__matrix[0][1] * self.__matrix[1][0]
									)
								else:
									a										=							[
									    self.__matrix[0][y] * self.cofactor(0		,      __magic_name__				) for y in range(self.__width				)
									]
									return sum(__magic_name__				)







def 		__A		(	__lowerCamelCase    )      ->       Matrix:
	a										=							[[0] * n for _ in range(__lowerCamelCase    )]
	return Matrix(__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )





def 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )      ->       Matrix:
	random.seed(__lowerCamelCase    )
	a										=							[
	    [random.randint(__lowerCamelCase							,			__lowerCamelCase    ) for _ in range(__lowerCamelCase    )] for _ in range(__lowerCamelCase    )
	]
	return Matrix(__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )







def 		__A		(	__lowerCamelCase							,			__lowerCamelCase    )      ->       str:
	if not isinstance(__lowerCamelCase							,			__lowerCamelCase    ):
		raise ValueError("""iterations must be defined as integers"""    )
	if not isinstance(__lowerCamelCase							,			__lowerCamelCase    ) or not number >= 1:
		raise ValueError(
		    """starting number must be
                         and integer and be more than 0"""    )
	if not iterations >= 1:
		raise ValueError("""Iterations must be done more than 0 times to play FizzBuzz"""    )

	a										=							""""""
	while number <= iterations:
		if number % 3 == 0:
			out += "Fizz"
		if number % 5 == 0:
			out += "Buzz"
		if 0 not in (number % 3, number % 5):
			out += str(__lowerCamelCase    )

		# print(out)
		number += 1
		out += " "
	return out


if __name__ == "__main__":
		import doctest

		doctest.testmod()

