

from maths.prime_factors import prime_factors




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






    if not isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        UpperCamelCase_			  =						f"Input value of [number={number}] must be an integer"
        raise TypeError(SCREAMING_SNAKE_CASE_			)
    if number < 1:
        raise ValueError("Input must be a positive integer"			)
    return -1 if len(prime_factors(SCREAMING_SNAKE_CASE_			)			) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()



def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list:



    """simple docstring"""






    if bit_count < 0:
        raise ValueError("The given input must be positive"			)

    # get the generated string sequence
    UpperCamelCase_			  =						gray_code_sequence_string(SCREAMING_SNAKE_CASE_			)
    #
    # convert them to integers
    for i in range(len(SCREAMING_SNAKE_CASE_			)			):
        UpperCamelCase_			  =						int(sequence[i]			,						2			)

    return sequence




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list:



    """simple docstring"""






    if bit_count == 0:
        return ["0"]

    if bit_count == 1:
        return ["0", "1"]

    UpperCamelCase_			  =						1 << bit_count  # defines the length of the sequence
    # 1<< n is equivalent to 2^n

    # recursive answer will generate answer for n-1 bits
    UpperCamelCase_			  =						gray_code_sequence_string(bit_count - 1			)

    UpperCamelCase_			  =						[]

    # append 0 to first half of the smaller sequence generated
    for i in range(seq_len // 2			):
        UpperCamelCase_			  =						"0" + smaller_sequence[i]
        sequence.append(SCREAMING_SNAKE_CASE_			)

    # append 1 to second half ... start from the end of the list
    for i in reversed(range(seq_len // 2			)			):
        UpperCamelCase_			  =						"1" + smaller_sequence[i]
        sequence.append(SCREAMING_SNAKE_CASE_			)

    return sequence


if __name__ == "__main__":
 import doctest

 doctest.testmod()
