






"""simple docstring"""





def   lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE					)					->	str:
    """simple docstring"""

    if number < 0 or shift_amount < 0:
        raise ValueError('both inputs must be positive integers'					)

    UpperCamelCase__         =    str(bin(SCREAMING_SNAKE_CASE					)					)
    binary_number += "0" * shift_amount
    return binary_number







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE					)					->	str:
    """simple docstring"""

    if number < 0 or shift_amount < 0:
        raise ValueError('both inputs must be positive integers'					)

    UpperCamelCase__         =    str(bin(SCREAMING_SNAKE_CASE					)					)[2:]
    if shift_amount >= len(SCREAMING_SNAKE_CASE					):
        return "0b0"
    UpperCamelCase__         =    binary_number[: len(SCREAMING_SNAKE_CASE					) - shift_amount]
    return "0b" + shifted_binary_number







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE					)					->	str:
    """simple docstring"""

    if number >= 0:  # Get binary representation of positive number
        UpperCamelCase__         =    '0' + str(bin(SCREAMING_SNAKE_CASE					)					).strip('-'					)[2:]
    else:  # Get binary (2's complement) representation of negative number
        UpperCamelCase__         =    len(bin(SCREAMING_SNAKE_CASE					)[3:]					)  # Find 2's complement of number
        UpperCamelCase__         =    bin(abs(SCREAMING_SNAKE_CASE					) - (1 << binary_number_length)					)[3:]
        UpperCamelCase__         =    (
            '1' + '0' * (binary_number_length - len(SCREAMING_SNAKE_CASE					)) + binary_number
        )

    if shift_amount >= len(SCREAMING_SNAKE_CASE					):
        return "0b" + binary_number[0] * len(SCREAMING_SNAKE_CASE					)
    return (
        "0b"
        + binary_number[0] * shift_amount
        + binary_number[: len(SCREAMING_SNAKE_CASE					) - shift_amount]
    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()












"""simple docstring"""





def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 50_00_00_00					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    set()
    UpperCamelCase__         =    int((limit - 24) ** (1 / 2)					)

    UpperCamelCase__         =    set(range(3 ,	prime_square_limit + 1 ,	2					)					)
    primes.add(2					)
    for p in range(3 ,	prime_square_limit + 1 ,	2					):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p ,	prime_square_limit + 1 ,	SCREAMING_SNAKE_CASE					)					)					)

    for primea in primes:
        UpperCamelCase__         =    primea * primea
        for primea in primes:
            UpperCamelCase__         =    primea * primea * primea
            if square + cube >= limit - 16:
                break
            for primea in primes:
                UpperCamelCase__         =    primea * primea * primea * primea
                UpperCamelCase__         =    square + cube + tetr
                if total >= limit:
                    break
                ret.add(SCREAMING_SNAKE_CASE					)

    return len(SCREAMING_SNAKE_CASE					)


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




