From the hint:

7 = 3 + 4 = 12

8 = 3 + 3 + 2 = 18

9 = 3 + 3 + 3 = 27

10 = 3 + 3 + 4 = 36

11 = 3 + 3 + 3 + 2 = 54

12 = 3 + 3 + 3 + 3 = 81

*Three* is a *magic* number.

```
class Solution(object):
def integerBreak(self, n):
if n == 2 or n == 3:
return n - 1
if n % 3 == 0:
return 3**(n/3)
if n % 3 == 1:
return 3**(n/3 - 1)*4
if n % 3 == 2:
return 3**(n/3)*2
```