"""
There are n oranges in the kitchen and you decided to eat some of these oranges every day as follows:

Eat one orange.
If the number of remaining oranges n is divisible by 2 then you can eat n / 2 oranges.
If the number of remaining oranges n is divisible by 3 then you can eat 2 * (n / 3) oranges.
You can only choose one of the actions per day.

Given the integer n, return the minimum number of days to eat n oranges.

Example 1:
Input: n = 10
Output: 4
Explanation: You have 10 oranges.
Day 1: Eat 1 orange,  10 - 1 = 9.
Day 2: Eat 6 oranges, 9 - 2*(9/3) = 9 - 6 = 3. (Since 9 is divisible by 3)
Day 3: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1.
Day 4: Eat the last orange  1 - 1  = 0.
You need at least 4 days to eat the 10 oranges.

Example 2:
Input: n = 6
Output: 3
Explanation: You have 6 oranges.
Day 1: Eat 3 oranges, 6 - 6/2 = 6 - 3 = 3. (Since 6 is divisible by 2).
Day 2: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1. (Since 3 is divisible by 3)
Day 3: Eat the last orange  1 - 1  = 0.
You need at least 3 days to eat the 6 oranges.


Constraints:
1 <= n <= 2 * 109

hint:
1 In each step, choose between 2 options: minOranges = 1 + min( (n%2) + f(n/2), (n%3) + f(n/3) ) where f(n) is the minimum number of days to eat n oranges.
"""
from functools import lru_cache


class MinimumNumberOfDaysToEatNOranges:
    @lru_cache(None)
    def minDays(self, n: int) -> int:
        if n <= 1:
            return n
        return 1 + min(n % 2 + self.minDays(n // 2), n % 3 + self.minDays(n // 3))
