



'''simple docstring'''
import math



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      int				):


			'''simple docstring'''







			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5							,							int(math.sqrt(lowerCamelCase__				) + 1				)							,							6				):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      int = 600851475143				):


			'''simple docstring'''







			try:
						A:      Optional[Any]														=   int(lowerCamelCase__				)
			except (TypeError, ValueError):
						raise TypeError("""Parameter n must be int or castable to int."""				)
			if n <= 0:
						raise ValueError("""Parameter n must be greater than or equal to one."""				)
			A:      Any														=   0
			if is_prime(lowerCamelCase__				):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase__				):
						return n
			for i in range(3							,							int(math.sqrt(lowerCamelCase__				)				) + 1							,							2				):
						if n % i == 0:
									if is_prime(n // i				):
												A:      Tuple														=   n // i
												break
									elif is_prime(lowerCamelCase__				):
												A:      List[Any]														=   i
			return max_number


if __name__ == "__main__":
					print(f"""{solution() = }""")










'''simple docstring'''
import numpy as np
import requests



def 		_SCREAMING_SNAKE_CASE							(				):


			'''simple docstring'''







			A:      List[Any]														=   requests.get(
			    """https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"""
			    """master/Week1/ADRvsRating.csv"""				)
			A:      List[str]														=   response.text.splitlines()
			A:      Dict														=   []
			for item in lines:
						A:      int														=   item.split(""","""				)
						data.append(lowerCamelCase__				)
			data.pop(0				)  # This is for removing the labels from the list
			A:      Tuple														=   np.matrix(lowerCamelCase__				)
			return dataset



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      Optional[Any]							,							lowerCamelCase__   :      List[str]							,							lowerCamelCase__   :      Optional[Any]							,							lowerCamelCase__   :      Dict							,							lowerCamelCase__   :      int				):


			'''simple docstring'''







			A:      Union[str, Any]														=   len_data

			A:      Tuple														=   np.dot(lowerCamelCase__							,							data_x.transpose()				)
			prod -= data_y.transpose()
			A:      Optional[Any]														=   np.dot(lowerCamelCase__							,							lowerCamelCase__				)
			A:      Optional[Any]														=   theta - (alpha / n) * sum_grad
			return theta



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      int							,							lowerCamelCase__   :      Optional[Any]							,							lowerCamelCase__   :      Union[str, Any]							,							lowerCamelCase__   :      Union[str, Any]				):


			'''simple docstring'''







			A:      str														=   np.dot(lowerCamelCase__							,							data_x.transpose()				)
			prod -= data_y.transpose()
			A:      Any														=   np.sum(np.square(lowerCamelCase__				)				)
			A:      List[Any]														=   sum_elem / (2 * len_data)
			return error



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      List[Any]							,							lowerCamelCase__   :      Union[str, Any]				):


			'''simple docstring'''







			A:      Dict														=   100000
			A:      Dict														=   0.0_00_15_50

			A:      Union[str, Any]														=   data_x.shape[1]
			A:      Tuple														=   data_x.shape[0] - 1

			A:      str														=   np.zeros((1, no_features)				)

			for i in range(0							,							lowerCamelCase__				):
						A:      List[str]														=   run_steep_gradient_descent(lowerCamelCase__							,							lowerCamelCase__							,							lowerCamelCase__							,							lowerCamelCase__							,							lowerCamelCase__				)
						A:      str														=   sum_of_square_error(lowerCamelCase__							,							lowerCamelCase__							,							lowerCamelCase__							,							lowerCamelCase__				)
						print(f'At Iteration {i + 1} - Error is {error:.5f}'				)

			return theta



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      List[Any]							,							lowerCamelCase__   :      List[str]				):


			'''simple docstring'''







			A:      List[Any]														=   sum(abs(y - predicted_y[i]				) for i, y in enumerate(lowerCamelCase__				)				)
			return total / len(lowerCamelCase__				)



def 		_SCREAMING_SNAKE_CASE							(				):


			'''simple docstring'''







			A:      Optional[Any]														=   collect_dataset()

			A:      str														=   data.shape[0]
			A:      Union[str, Any]														=   np.c_[np.ones(lowerCamelCase__				), data[:, :-1]].astype(lowerCamelCase__				)
			A:      Any														=   data[:, -1].astype(lowerCamelCase__				)

			A:      Dict														=   run_linear_regression(lowerCamelCase__							,							lowerCamelCase__				)
			A:      Union[str, Any]														=   theta.shape[1]
			print("""Resultant Feature vector : """				)
			for i in range(0							,							lowerCamelCase__				):
						print(f'{theta[0, i]:.5f}'				)


if __name__ == "__main__":
					main()





