"""

if not isinstance(a, int):

raise TypeError(f"Must be int, not {type(a).__name__}")

if a < 1:

raise ValueError(f"Given integer must be greater than 1, not {a}")

path = [a]

while a != 1:

if a % 2 == 0:

a = a // 2

else:

a = 3 * a + 1

path += [a]

"""

assert n31(4) == ([4, 2, 1], 3)

assert n31(11) == ([11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1], 15)

assert n31(31) == (

[

31,

94,

47,

142,

71,

214,

107,

322,

161,

484,

242,

121,

364,

182,

91,

274,

137,

412,

206,

103,

310,

155,

466,

233,

700,

350,

175,

526,

263,

790,

395,

1186,

593,

1780,

890,

445,

1336,

668,

334,

167,

502,

251,

754,

377,

1132,

566,

283,

850,

425,

1276,

638,

319,

958,

479,

1438,

719,

2158,

1079,

3238,

1619,

4858,

2429,

7288,

3644,

1822,

911,

2734,

1367,

4102,

2051,

6154,

3077,

9232,

4616,

2308,

1154,

577,

1732,

866,

433,

1300,

650,

325,

976,

488,

244,

122,

61,

184,

92,

46,

23,

70,

35,

106,

53,

160,

80,

40,

20,

10,

5,

16,

8,

4,

2,

1,

],

107,