

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__       (      a__			,      a__			,      a__)		->    list:



    """simple docstring"""







    seed(1)
    return [gauss(a__			,      a__) for _ in range(a__)]

def   lowerCamelCase__       (      a__			,      a__)		->    list:



    """simple docstring"""







    return [k for k in range(a__) for _ in range(instance_count[k])]

def   lowerCamelCase__       (      a__			,      a__)		->    float:



    """simple docstring"""







    return sum(a__) / instance_count

def   lowerCamelCase__       (      a__			,      a__)		->    float:



    """simple docstring"""







    return instance_count / total_count

def   lowerCamelCase__       (      a__			,      a__			,      a__)		->    float:



    """simple docstring"""







    _snake_case : Optional[Any]												=		[]  # An empty list to store all squared differences
    # iterate over number of elements in items
    for i in range(len(a__)):
        # 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
    _snake_case : Union[str, Any]												=		len(a__)  # Number of classes in dataset
    return 1 / (total_count - n_classes) * sum(a__)

def   lowerCamelCase__       (      a__			,      a__			,      a__			,      a__)		->    list:



    """simple docstring"""







    _snake_case : int												=		[]
    # for loop iterates over number of elements in list
    for i in range(len(a__)):
        # for loop iterates over number of inner items of each element
        for j in range(len(x_items[i])):
            _snake_case : List[Any]												=		[]  # 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(a__)):
                # 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(a__)

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

def   lowerCamelCase__       (      a__			,      a__)		->    float:



    """simple docstring"""







    _snake_case : str												=		sum(1 for i, j in zip(a__			,      a__) 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(a__)) * 1_0_0


SCREAMING_SNAKE_CASE_    =   TypeVar("num")

def   lowerCamelCase__       (      a__			,      a__			,      a__			,      a__ = lambda a__: True			,      a__ = None			,      )		->    num:



    """simple docstring"""







    while True:
        try:
            _snake_case : List[str]												=		input_type(input(a__).strip() or default)
            if condition(a__):
                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__       (      )		->    int:



    """simple docstring"""







    while True:
        print(' Linear Discriminant Analysis '.center(5_0			,      '*'))
        print('*' * 5_0			,      '\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
        _snake_case : Optional[Any]												=		valid_input(
            input_type=a__			,      condition=lambda a__: x > 0			,      input_msg='Enter the number of classes (Data Groupings): '			,      err_msg='Number of classes should be positive!'			,      )

        print('-' * 1_0_0)

        # Trying to get the value of standard deviation
        _snake_case : Union[str, Any]												=		valid_input(
            input_type=a__			,      condition=lambda a__: 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_0_0)

        # Trying to get number of instances in classes and theirs means to generate
        # dataset
        _snake_case : Dict												=		[]  # An empty list to store instance counts of classes in dataset
        for i in range(a__):
            _snake_case : Union[str, Any]												=		valid_input(
                input_type=a__			,      condition=lambda a__: x > 0			,      input_msg=(F"""Enter The number of instances for class_{i+1}: """)			,      err_msg='Number of instances should be positive!'			,      )
            counts.append(a__)
        print('-' * 1_0_0)

        # An empty list to store values of user-entered means of classes
        _snake_case : Union[str, Any]												=		[]
        for a in range(a__):
            _snake_case : Any												=		valid_input(
                input_type=a__			,      input_msg=(F"""Enter the value of mean for class_{a+1}: """)			,      err_msg='This is an invalid value.'			,      )
            user_means.append(a__)
        print('-' * 1_0_0)

        print('Standard deviation: '			,      a__)
        # print out the number of instances in classes in separated line
        for i, count in enumerate(a__			,      1):
            print(F"""Number of instances in class_{i} is: {count}""")
        print('-' * 1_0_0)

        # print out mean values of classes separated line
        for i, user_mean in enumerate(a__			,      1):
            print(F"""Mean of class_{i} is: {user_mean}""")
        print('-' * 1_0_0)

        # Generating training dataset drawn from gaussian distribution
        _snake_case : Optional[Any]												=		[
            gaussian_distribution(user_means[j]			,      a__			,      counts[j])
            for j in range(a__)
        ]
        print('Generated Normal Distribution: \n'			,      a__)
        print('-' * 1_0_0)

        # Generating Ys to detecting corresponding classes
        _snake_case : Optional[Any]												=		y_generator(a__			,      a__)
        print('Generated Corresponding Ys: \n'			,      a__)
        print('-' * 1_0_0)

        # Calculating the value of actual mean for each class
        _snake_case : Union[str, Any]												=		[calculate_mean(counts[k]			,      x[k]) for k in range(a__)]
        # for loop iterates over number of elements in 'actual_means' list and print
        # out them in separated line
        for i, actual_mean in enumerate(a__			,      1):
            print(F"""Actual(Real) mean of class_{i} is: {actual_mean}""")
        print('-' * 1_0_0)

        # Calculating the value of probabilities for each class
        _snake_case : Dict												=		[
            calculate_probabilities(counts[i]			,      sum(a__)) for i in range(a__)
        ]

        # for loop iterates over number of elements in 'probabilities' list and print
        # out them in separated line
        for i, probability in enumerate(a__			,      1):
            print(F"""Probability of class_{i} is: {probability}""")
        print('-' * 1_0_0)

        # Calculating the values of variance for each class
        _snake_case : Any												=		calculate_variance(a__			,      a__			,      sum(a__))
        print('Variance: '			,      a__)
        print('-' * 1_0_0)

        # Predicting Y values
        # storing predicted Y values in 'pre_indexes' variable
        _snake_case : Dict												=		predict_y_values(a__			,      a__			,      a__			,      a__)
        print('-' * 1_0_0)

        # Calculating Accuracy of the model
        print(F"""Accuracy: {accuracy(a__			,      a__)}""")
        print('-' * 1_0_0)
        print(' DONE '.center(1_0_0			,      '+'))

        if input('Press any key to restart or \'q\' for quit: ').strip().lower() == "q":
            print('\n' + 'GoodBye!'.center(1_0_0			,      '-') + '\n')
            break
        system('cls' if name == 'nt' else 'clear')  # noqa: S605


if __name__ == "__main__":
   main()






'''simple docstring'''



from __future__ import annotations

from collections import Counter

def   lowerCamelCase__       (      a__)		->    list[int]:



    """simple docstring"""







    _snake_case : Optional[int]												=		[True] * n
    _snake_case : List[str]												=		False
    _snake_case : int												=		False
    _snake_case : Tuple												=		True

    for i in range(3			,      int(n**0.5 + 1)			,      2):
        _snake_case : int												=		i * 2
        while index < n:
            _snake_case : List[str]												=		False
            _snake_case : Union[str, Any]												=		index + i

    _snake_case : List[str]												=		[2]

    for i in range(3			,      a__			,      2):
        if is_prime[i]:
            primes.append(a__)

    return primes

def   lowerCamelCase__       (      a__)		->    list[list[int]]:



    """simple docstring"""







    _snake_case : Tuple												=		str(a__)
    _snake_case : str												=		[]
    _snake_case : Union[str, Any]												=		['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']

    for duplicate in Counter(a__) - Counter(set(a__)):
        _snake_case : List[Any]												=		[int(number_str.replace(a__			,      a__)) for digit in digits]
        replacements.append(a__)

    return replacements

def   lowerCamelCase__       (      a__ = 8)		->    int:



    """simple docstring"""







    _snake_case : Any												=		set()

    # Filter primes with less than 3 replaceable digits
    _snake_case : List[Any]												=		{
        x for x in set(prime_sieve(1_0_0_0_0_0_0)) if len(str(a__)) - len(set(str(a__))) >= 3
    }

    for prime in primes:
        if prime in numbers_checked:
            continue

        _snake_case : int												=		digit_replacements(a__)

        for family in replacements:
            numbers_checked.update(a__)
            _snake_case : Union[str, Any]												=		primes.intersection(a__)

            if len(a__) != family_length:
                continue

            return min(a__)

    return -1


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



