






"""simple docstring"""





A__					: Any=	{
    0: """0""",
    1: """1""",
    2: """2""",
    3: """3""",
    4: """4""",
    5: """5""",
    6: """6""",
    7: """7""",
    8: """8""",
    9: """9""",
    10: """a""",
    11: """b""",
    12: """c""",
    13: """d""",
    14: """e""",
    15: """f""",
}







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

    assert type(SCREAMING_SNAKE_CASE					) in (int, float) and decimal == int(SCREAMING_SNAKE_CASE					)
    UpperCamelCase__         =    int(SCREAMING_SNAKE_CASE					)
    UpperCamelCase__         =    ''
    UpperCamelCase__         =    False
    if decimal < 0:
        UpperCamelCase__         =    True
        decimal *= -1
    while decimal > 0:
        UpperCamelCase__       ,						UpperCamelCase__         =    divmod(SCREAMING_SNAKE_CASE ,	16					)
        UpperCamelCase__         =    values[remainder] + hexadecimal
    UpperCamelCase__         =    '0x' + hexadecimal
    if negative:
        UpperCamelCase__         =    '-' + hexadecimal
    return hexadecimal


if __name__ == "__main__":
  import doctest

  doctest.testmod()












"""simple docstring"""





def   lowerCAmelCase_( SCREAMING_SNAKE_CASE					)					->	bool:
    """simple docstring"""

    UpperCamelCase__         =    (1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 50_00					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    [(i * (3 * i - 1)) // 2 for i in range(1 ,	SCREAMING_SNAKE_CASE					)]
    for i, pentagonal_i in enumerate(SCREAMING_SNAKE_CASE					):
        for j in range(SCREAMING_SNAKE_CASE ,	len(SCREAMING_SNAKE_CASE					)					):
            UpperCamelCase__         =    pentagonal_nums[j]
            UpperCamelCase__         =    pentagonal_i + pentagonal_j
            UpperCamelCase__         =    pentagonal_j - pentagonal_i
            if is_pentagonal(SCREAMING_SNAKE_CASE					) and is_pentagonal(SCREAMING_SNAKE_CASE					):
                return b

    return -1


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




