import math
import random







def 						A__  (					__A   , __A = False	):







    '''simple docstring'''
    if deriv:
        return value * (1 - value)
    return 1 / (1 + math.exp(-value	))


# Initial Value
lowerCAmelCase			:							Optional[int]     =0.02







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Optional[int] 						=						float(2 * (random.randint(1   , 100	)) - 1	)

    for _ in range(__A	):
        # Forward propagation
        _lowerCamelCase     :		Dict 						=						sigmoid_function(INITIAL_VALUE * weight	)
        # How much did we miss?
        _lowerCamelCase     :		Optional[int] 						=						(expected / 100) - layer_a
        # Error delta
        _lowerCamelCase     :		List[Any] 						=						layer_1_error * sigmoid_function(__A   , __A	)
        # Update weight
        weight += INITIAL_VALUE * layer_1_delta

    return layer_a * 100


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    lowerCAmelCase			:							Optional[int]     =int(input("Expected value: "))
    lowerCAmelCase			:							Any     =int(input("Number of propagations: "))
    print(forward_propagation(expected, number_propagations))





from __future__ import annotations

lowerCAmelCase			:							int     =[]







def 						A__  (					__A   , __A   , __A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        if board[row][i] == 1:
            return False
    for i in range(len(__A	)	):
        if board[i][column] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , -1   , -1	)	):
        if board[i][j] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , len(__A	)	)	):
        if board[i][j] == 1:
            return False
    return True







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    if row >= len(__A	):
        solution.append(__A	)
        printboard(__A	)
        print()
        return True
    for i in range(len(__A	)	):
        if is_safe(__A   , __A   , __A	):
            _lowerCamelCase     :		int 						=						1
            solve(__A   , row + 1	)
            _lowerCamelCase     :		List[str] 						=						0
    return False







def 						A__  (					__A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        for j in range(len(__A	)	):
            if board[i][j] == 1:
                print("""Q"""   , end=""" """	)
            else:
                print("""."""   , end=""" """	)
        print()


# n=int(input("The no. of queens"))
lowerCAmelCase			:							int     =8
lowerCAmelCase			:							Union[str, Any]     =[[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print("The total no. of solutions are :", len(solution))




