

"""simple docstring"""




from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					seed(1 )
					return [gauss(lowercase__     ,				lowercase__ ) for _ in range(lowercase__ )]
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					return [k for k in range(lowercase__ ) for _ in range(instance_count[k] )]
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					return sum(lowercase__ ) / instance_count
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					return instance_count / total_count
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     =   []  # An empty list to store all squared differences
					# iterate over number of elements in items
					for i in range(len(lowercase__ ) ):
										# for loop iterates over number of elements in inner layer of items
										for j in range(len(items[i] ) ):
															# appending squared differences to 'squared_diff' list
															squared_diff.append((items[i][j] - means[i]) ** 2 )

    # one divided by (the number of all instances - number of classes) multiplied by
    # sum of all squared differences
					A     =   len(lowercase__ )  # Number of classes in dataset
					return 1 / (total_count - n_classes) * sum(lowercase__ )
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     =   []
					# for loop iterates over number of elements in list
					for i in range(len(lowercase__ ) ):
										# for loop iterates over number of inner items of each element
										for j in range(len(x_items[i] ) ):
															A     =   []  # to store all discriminant values of each item as a list
															# for loop iterates over number of classes we have in our dataset
															for k in range(len(lowercase__ ) ):
																				# appending values of discriminants for each class to 'temp' list
																				temp.append(
																				    x_items[i][j] * (means[k] / variance)
																				    - (means[k] ** 2 / (2 * variance))
																				    + log(probabilities[k] ) )
															# appending discriminant values of each item to 'results' list
															results.append(lowercase__ )

					return [result.index(max(lowercase__ ) ) for result in results]
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     =   sum(1 for i, j in zip(lowercase__     ,				lowercase__ ) if i == j )
					# percentage of accuracy equals to number of correct predictions divided by number
					# of all data and multiplied by 100
					return (correct / len(lowercase__ )) * 100


__A	:       Optional[int]        =						TypeVar('num')
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__ = lambda lowercase__ : True     ,				lowercase__ = None     ,				):
					"""simple docstring"""
					while True:
										try:
															A     =   input_type(input(lowercase__ ).strip() or default )
															if condition(lowercase__ ):
																				return user_input
															else:
																				print(F"""{user_input}: {err_msg}""" )
																				continue
										except ValueError:
															print(
															    F"""{user_input}: Incorrect input type, expected {input_type.__name__!r}""" )
def   __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					while True:
										print(" Linear Discriminant Analysis ".center(50     ,				"*" ) )
										print("*" * 50     ,				"\n" )
										print("First of all we should specify the number of classes that" )
										print("we want to generate as training dataset" )
										# Trying to get number of classes
										A     =   valid_input(
										    input_type=lowercase__     ,				condition=lambda lowercase__ : x > 0     ,				input_msg="Enter the number of classes (Data Groupings): "     ,				err_msg="Number of classes should be positive!"     ,				)

										print("-" * 100 )

										# Trying to get the value of standard deviation
										A     =   valid_input(
										    input_type=lowercase__     ,				condition=lambda lowercase__ : x >= 0     ,				input_msg=(
										        "Enter the value of standard deviation"
										        "(Default value is 1.0 for all classes): "
										    )     ,				err_msg="Standard deviation should not be negative!"     ,				default="1.0"     ,				)

										print("-" * 100 )

										# Trying to get number of instances in classes and theirs means to generate
										# dataset
										A     =   []  # An empty list to store instance counts of classes in dataset
										for i in range(lowercase__ ):
															A     =   valid_input(
															    input_type=lowercase__     ,				condition=lambda lowercase__ : x > 0     ,				input_msg=(F"""Enter The number of instances for class_{i+1}: """)     ,				err_msg="Number of instances should be positive!"     ,				)
															counts.append(lowercase__ )
										print("-" * 100 )

										# An empty list to store values of user-entered means of classes
										A     =   []
										for a in range(lowercase__ ):
															A     =   valid_input(
															    input_type=lowercase__     ,				input_msg=(F"""Enter the value of mean for class_{a+1}: """)     ,				err_msg="This is an invalid value."     ,				)
															user_means.append(lowercase__ )
										print("-" * 100 )

										print("Standard deviation: "     ,				lowercase__ )
										# print out the number of instances in classes in separated line
										for i, count in enumerate(lowercase__     ,				1 ):
															print(F"""Number of instances in class_{i} is: {count}""" )
										print("-" * 100 )

										# print out mean values of classes separated line
										for i, user_mean in enumerate(lowercase__     ,				1 ):
															print(F"""Mean of class_{i} is: {user_mean}""" )
										print("-" * 100 )

										# Generating training dataset drawn from gaussian distribution
										A     =   [
										    gaussian_distribution(user_means[j]     ,				lowercase__     ,				counts[j] )
										    for j in range(lowercase__ )
										]
										print("Generated Normal Distribution: \n"     ,				lowercase__ )
										print("-" * 100 )

										# Generating Ys to detecting corresponding classes
										A     =   y_generator(lowercase__     ,				lowercase__ )
										print("Generated Corresponding Ys: \n"     ,				lowercase__ )
										print("-" * 100 )

										# Calculating the value of actual mean for each class
										A     =   [calculate_mean(counts[k]     ,				x[k] ) for k in range(lowercase__ )]
										# for loop iterates over number of elements in 'actual_means' list and print
										# out them in separated line
										for i, actual_mean in enumerate(lowercase__     ,				1 ):
															print(F"""Actual(Real) mean of class_{i} is: {actual_mean}""" )
										print("-" * 100 )

										# Calculating the value of probabilities for each class
										A     =   [
										    calculate_probabilities(counts[i]     ,				sum(lowercase__ ) ) for i in range(lowercase__ )
										]

										# for loop iterates over number of elements in 'probabilities' list and print
										# out them in separated line
										for i, probability in enumerate(lowercase__     ,				1 ):
															print(F"""Probability of class_{i} is: {probability}""" )
										print("-" * 100 )

										# Calculating the values of variance for each class
										A     =   calculate_variance(lowercase__     ,				lowercase__     ,				sum(lowercase__ ) )
										print("Variance: "     ,				lowercase__ )
										print("-" * 100 )

										# Predicting Y values
										# storing predicted Y values in 'pre_indexes' variable
										A     =   predict_y_values(lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__ )
										print("-" * 100 )

										# Calculating Accuracy of the model
										print(F"""Accuracy: {accuracy(lowercase__     ,				lowercase__ )}""" )
										print("-" * 100 )
										print(" DONE ".center(100     ,				"+" ) )

										if input("Press any key to restart or 'q' for quit: " ).strip().lower() == "q":
															print("\n" + "GoodBye!".center(100     ,				"-" ) + "\n" )
															break
										system("cls" if name == "nt" else "clear" )  # noqa: S605


if __name__ == "__main__":
	main()











def    snake_case   (				A		,  A     )				->				int:




	'''simple docstring'''


	if a < b:
		return gcd(A		,  A     )
	if a % b == 0:
		return b
	return gcd(A		,  a % b     )






def    snake_case   (				A		,  A		,  A     )				->				int:




	'''simple docstring'''


	if y == 0:
		return 1
	lowerCamelCase_				:						int				  =				power(A		,  y // 2		,  A     ) % mod
	lowerCamelCase_				:						List[Any]				  =				(temp * temp) % mod
	if y % 2 == 1:
		lowerCamelCase_				:						str				  =				(temp * x) % mod
	return temp






def    snake_case   (				A     )				->				bool:




	'''simple docstring'''


	lowerCamelCase_				:						Union[str, Any]				  =				2
	while b < n:
		if gcd(A		,  A     ) == 1 and power(A		,  n - 1		,  A     ) != 1:
			return False
		b += 1
	return True


if __name__ == "__main__":
							UpperCamelCase__						=		int(input('Enter number: ').strip())
							if is_carmichael_number(number):
														print(F'{number} is a Carmichael Number.')
							else:
														print(F'{number} is not a Carmichael Number.')
