




'''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      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__		):
			seed(1		)
			return [gauss(_UpperCamelCase   , _UpperCamelCase		) for _ in range(_UpperCamelCase		)]

def      __lowerCAmelCase   (       snake_case__   , snake_case__		):
			return [k for k in range(_UpperCamelCase		) for _ in range(instance_count[k]		)]

def      __lowerCAmelCase   (       snake_case__   , snake_case__		):
			return sum(_UpperCamelCase		) / instance_count

def      __lowerCAmelCase   (       snake_case__   , snake_case__		):
			return instance_count / total_count

def      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__		):
			__UpperCamelCase :     Dict										=  []  # An empty list to store all squared differences
			# iterate over number of elements in items
			for i in range(len(_UpperCamelCase		)		):
						# 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
			__UpperCamelCase :     Any										=  len(_UpperCamelCase		)  # Number of classes in dataset
			return 1 / (total_count - n_classes) * sum(_UpperCamelCase		)

def      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__   , snake_case__		):
			__UpperCamelCase :     Optional[int]										=  []
			# for loop iterates over number of elements in list
			for i in range(len(_UpperCamelCase		)		):
						# for loop iterates over number of inner items of each element
						for j in range(len(x_items[i]		)		):
									__UpperCamelCase :     Optional[int]										=  []  # 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(_UpperCamelCase		)		):
												# 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(_UpperCamelCase		)

			return [result.index(max(_UpperCamelCase		)		) for result in results]

def      __lowerCAmelCase   (       snake_case__   , snake_case__		):
			__UpperCamelCase :     str										=  sum(1 for i, j in zip(_UpperCamelCase   , _UpperCamelCase		) 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(_UpperCamelCase		)) * 100


_lowerCAmelCase       =   TypeVar('''num''')

def      __lowerCAmelCase   (       snake_case__   , snake_case__   , snake_case__   , snake_case__ = lambda snake_case__		: True   , snake_case__ = None   , ):
			while True:
						try:
									__UpperCamelCase :     int										=  input_type(input(_UpperCamelCase		).strip() or default		)
									if condition(_UpperCamelCase		):
												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      __lowerCAmelCase   (       ):
			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
						__UpperCamelCase :     str										=  valid_input(
						    input_type=_UpperCamelCase   , condition=lambda snake_case__		: 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
						__UpperCamelCase :     str										=  valid_input(
						    input_type=_UpperCamelCase   , 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("-" * 100		)

						# Trying to get number of instances in classes and theirs means to generate
						# dataset
						__UpperCamelCase :     Tuple										=  []  # An empty list to store instance counts of classes in dataset
						for i in range(_UpperCamelCase		):
									__UpperCamelCase :     Optional[int]										=  valid_input(
									    input_type=_UpperCamelCase   , 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(_UpperCamelCase		)
						print("-" * 100		)

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

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

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

						# Generating Ys to detecting corresponding classes
						__UpperCamelCase :     Optional[Any]										=  y_generator(_UpperCamelCase   , _UpperCamelCase		)
						print("Generated Corresponding Ys: \n"   , _UpperCamelCase		)
						print("-" * 100		)

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

						# Calculating the value of probabilities for each class
						__UpperCamelCase :     int										=  [
						    calculate_probabilities(counts[i]   , sum(_UpperCamelCase		)		) for i in range(_UpperCamelCase		)
						]

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

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

						# Predicting Y values
						# storing predicted Y values in 'pre_indexes' variable
						__UpperCamelCase :     int										=  predict_y_values(_UpperCamelCase   , _UpperCamelCase   , _UpperCamelCase   , _UpperCamelCase		)
						print("-" * 100		)

						# Calculating Accuracy of the model
						print(F"Accuracy: {accuracy(_UpperCamelCase   , _UpperCamelCase		)}"		)
						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()





"""simple docstring"""







def        __lowerCAmelCase							(_UpperCamelCase = 10**6						):

	if n <= 0:
		raise ValueError('Please enter an integer greater than 0'						)

	__lowerCAmelCase     :		Optional[Any]		     = list(range(n + 1						)						)
	for number in range(2			,    n + 1						):
		if phi[number] == number:
			phi[number] -= 1
			for multiple in range(number * 2			,    n + 1			,    _UpperCamelCase						):
				__lowerCAmelCase     :		Tuple		     = (phi[multiple] // number) * (number - 1)

	__lowerCAmelCase     :		Any		     = 1
	for number in range(1			,    n + 1						):
		if (answer / phi[answer]) < (number / phi[number]):
			__lowerCAmelCase     :		List[Any]		     = number

	return answer


if __name__ == "__main__":
							print(solution())