


from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar
def 							UpperCamelCase_  (				__snake_case			:						float	,			__snake_case			:						float	,			__snake_case			:						int     )->      list:




						'''simple docstring'''
						seed(1     )
						return [gauss(__snake_case	,			__snake_case     ) for _ in range(__snake_case     )]
def 							UpperCamelCase_  (				__snake_case			:						int	,			__snake_case			:						list     )->      list:




						'''simple docstring'''
						return [k for k in range(__snake_case     ) for _ in range(instance_count[k]     )]
def 							UpperCamelCase_  (				__snake_case			:						int	,			__snake_case			:						list     )->      float:




						'''simple docstring'''
						return sum(__snake_case     ) / instance_count
def 							UpperCamelCase_  (				__snake_case			:						int	,			__snake_case			:						int     )->      float:




						'''simple docstring'''
						return instance_count / total_count
def 							UpperCamelCase_  (				__snake_case			:						list	,			__snake_case			:						list	,			__snake_case			:						int     )->      float:




						'''simple docstring'''
						__magic_name__ 		=			[]  # An empty list to store all squared differences
						# iterate over number of elements in items
						for i in range(len(__snake_case     )     ):
												# 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
						__magic_name__ 		=			len(__snake_case     )  # Number of classes in dataset
						return 1 / (total_count - n_classes) * sum(__snake_case     )
def 							UpperCamelCase_  (				__snake_case			:						list	,			__snake_case			:						list	,			__snake_case			:						float	,			__snake_case			:						list     )->      list:




						'''simple docstring'''
						__magic_name__ 		=			[]
						# for loop iterates over number of elements in list
						for i in range(len(__snake_case     )     ):
												# for loop iterates over number of inner items of each element
												for j in range(len(x_items[i]     )     ):
																		__magic_name__ 		=			[]  # 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(__snake_case     )     ):
																								# 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(__snake_case     )

						return [result.index(max(__snake_case     )     ) for result in results]
def 							UpperCamelCase_  (				__snake_case			:						list	,			__snake_case			:						list     )->      float:




						'''simple docstring'''
						__magic_name__ 		=			sum(1 for i, j in zip(__snake_case	,			__snake_case     ) 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(__snake_case     )) * 1_00


UpperCamelCase :				str						    =       TypeVar('''num''')
def 							UpperCamelCase_  (				__snake_case			:						Callable[[object], num]	,			__snake_case			:						str	,			__snake_case			:						str	,			__snake_case			:						Callable[[num], bool] = lambda __snake_case     : True	,			__snake_case			:						str | None = None	,			)->      num:




						'''simple docstring'''
						while True:
												try:
																		__magic_name__ 		=			input_type(input(__snake_case     ).strip() or default     )
																		if condition(__snake_case     ):
																								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 							UpperCamelCase_  (				)->      Union[str, Any]:




						'''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
												__magic_name__ 		=			valid_input(
												    input_type=__snake_case	,			condition=lambda __snake_case     : x > 0	,			input_msg='Enter the number of classes (Data Groupings): '	,			err_msg='Number of classes should be positive!'	,			)

												print('-' * 1_00     )

												# Trying to get the value of standard deviation
												__magic_name__ 		=			valid_input(
												    input_type=__snake_case	,			condition=lambda __snake_case     : 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('-' * 1_00     )

												# Trying to get number of instances in classes and theirs means to generate
												# dataset
												__magic_name__ 		=			[]  # An empty list to store instance counts of classes in dataset
												for i in range(__snake_case     ):
																		__magic_name__ 		=			valid_input(
																		    input_type=__snake_case	,			condition=lambda __snake_case     : x > 0	,			input_msg=(F'''Enter The number of instances for class_{i+1}: ''')	,			err_msg='Number of instances should be positive!'	,			)
																		counts.append(__snake_case     )
												print('-' * 1_00     )

												# An empty list to store values of user-entered means of classes
												__magic_name__ 		=			[]
												for a in range(__snake_case     ):
																		__magic_name__ 		=			valid_input(
																		    input_type=__snake_case	,			input_msg=(F'''Enter the value of mean for class_{a+1}: ''')	,			err_msg='This is an invalid value.'	,			)
																		user_means.append(__snake_case     )
												print('-' * 1_00     )

												print('Standard deviation: '	,			__snake_case     )
												# print out the number of instances in classes in separated line
												for i, count in enumerate(__snake_case	,			1     ):
																		print(F'''Number of instances in class_{i} is: {count}'''     )
												print('-' * 1_00     )

												# print out mean values of classes separated line
												for i, user_mean in enumerate(__snake_case	,			1     ):
																		print(F'''Mean of class_{i} is: {user_mean}'''     )
												print('-' * 1_00     )

												# Generating training dataset drawn from gaussian distribution
												__magic_name__ 		=			[
												    gaussian_distribution(user_means[j]	,			__snake_case	,			counts[j]     )
												    for j in range(__snake_case     )
												]
												print('Generated Normal Distribution: \n'	,			__snake_case     )
												print('-' * 1_00     )

												# Generating Ys to detecting corresponding classes
												__magic_name__ 		=			y_generator(__snake_case	,			__snake_case     )
												print('Generated Corresponding Ys: \n'	,			__snake_case     )
												print('-' * 1_00     )

												# Calculating the value of actual mean for each class
												__magic_name__ 		=			[calculate_mean(counts[k]	,			x[k]     ) for k in range(__snake_case     )]
												# for loop iterates over number of elements in 'actual_means' list and print
												# out them in separated line
												for i, actual_mean in enumerate(__snake_case	,			1     ):
																		print(F'''Actual(Real) mean of class_{i} is: {actual_mean}'''     )
												print('-' * 1_00     )

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

												# for loop iterates over number of elements in 'probabilities' list and print
												# out them in separated line
												for i, probability in enumerate(__snake_case	,			1     ):
																		print(F'''Probability of class_{i} is: {probability}'''     )
												print('-' * 1_00     )

												# Calculating the values of variance for each class
												__magic_name__ 		=			calculate_variance(__snake_case	,			__snake_case	,			sum(__snake_case     )     )
												print('Variance: '	,			__snake_case     )
												print('-' * 1_00     )

												# Predicting Y values
												# storing predicted Y values in 'pre_indexes' variable
												__magic_name__ 		=			predict_y_values(__snake_case	,			__snake_case	,			__snake_case	,			__snake_case     )
												print('-' * 1_00     )

												# Calculating Accuracy of the model
												print(F'''Accuracy: {accuracy(__snake_case	,			__snake_case     )}'''     )
												print('-' * 1_00     )
												print(' DONE '.center(1_00	,			'+'     )     )

												if input('Press any key to restart or \'q\' for quit: '     ).strip().lower() == "q":
																		print('\n' + 'GoodBye!'.center(1_00	,			'-'     ) + '\n'     )
																		break
												system('cls' if name == 'nt' else 'clear'     )  # noqa: S605


if __name__ == "__main__":
					main()





def 							UpperCamelCase_  (				__snake_case			:						int = 1_00     )->      int:




						'''simple docstring'''
						__magic_name__ 		=			1
						__magic_name__ 		=			0
						for i in range(1	,			num + 1     ):
												fact *= i

						for j in str(__snake_case     ):
												result += int(__snake_case     )

						return result


if __name__ == "__main__":
					print(solution(int(input('''Enter the Number: ''').strip())))

