
__magic_name__           =					{
    '''0''': 1,
    '''1''': 1,
    '''2''': 2,
    '''3''': 6,
    '''4''': 24,
    '''5''': 120,
    '''6''': 720,
    '''7''': 5_040,
    '''8''': 40_320,
    '''9''': 362_880,
}

__magic_name__           =					{145: 145}

__magic_name__           =					{
    145: 0,
    169: 3,
    36_301: 3,
    1_454: 3,
    871: 2,
    45_361: 2,
    872: 2,
}





def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase							):
    if n in CACHE_SUM_DIGIT_FACTORIALS:
        return CACHE_SUM_DIGIT_FACTORIALS[n]
    snake_case__  =			sum(DIGIT_FACTORIALS[let] for let in str(__lowerCAmelCase							)							)
    snake_case__  =			ret
    return ret





def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase      ,						__lowerCAmelCase = None							):
    snake_case__  =			previous or set()
    if n in CHAIN_LENGTH_CACHE:
        return CHAIN_LENGTH_CACHE[n]
    snake_case__  =			sum_digit_factorials(__lowerCAmelCase							)
    if next_number in previous:
        snake_case__  =			0
        return 0
    else:
        previous.add(__lowerCAmelCase							)
        snake_case__  =			1 + chain_length(__lowerCAmelCase      ,						__lowerCAmelCase							)
        snake_case__  =			ret
        return ret





def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase = 60      ,						__lowerCAmelCase = 1_000_000							):
    return sum(1 for i in range(1      ,						__lowerCAmelCase							) if chain_length(__lowerCAmelCase							) == num_terms							)


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





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__      ( __lowerCAmelCase      ,						__lowerCAmelCase      ,						__lowerCAmelCase							):
    seed(1							)
    return [gauss(__lowerCAmelCase      ,						__lowerCAmelCase							) for _ in range(__lowerCAmelCase							)]





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





def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase      ,						__lowerCAmelCase							):
    return sum(__lowerCAmelCase							) / instance_count





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





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





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

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





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


__magic_name__           =					TypeVar('''num''')





def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase      ,						__lowerCAmelCase      ,						__lowerCAmelCase      ,						__lowerCAmelCase = lambda __lowerCAmelCase							: True      ,						__lowerCAmelCase = None      ,						):
    while True:
        try:
            snake_case__  =			input_type(input(__lowerCAmelCase							).strip() or default							)
            if condition(__lowerCAmelCase							):
                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__      ( ):
    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
        snake_case__  =			valid_input(
            input_type=__lowerCAmelCase      ,						condition=lambda __lowerCAmelCase							: 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
        snake_case__  =			valid_input(
            input_type=__lowerCAmelCase      ,						condition=lambda __lowerCAmelCase							: 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
        snake_case__  =			[]  # An empty list to store instance counts of classes in dataset
        for i in range(__lowerCAmelCase							):
            snake_case__  =			valid_input(
                input_type=__lowerCAmelCase      ,						condition=lambda __lowerCAmelCase							: x > 0      ,						input_msg=(F"""Enter The number of instances for class_{i+1}: """)      ,						err_msg="Number of instances should be positive!"      ,						)
            counts.append(__lowerCAmelCase							)
        print("-" * 100							)

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

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

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

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

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

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

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

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

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

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



