Minimum Number of Days to Eat N Oranges

lcpy gen -n 1553   # by problem number
lcpy gen -s minimum_number_of_days_to_eat_n_oranges   # by problem name

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.

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.

from functools import cache


class Solution:
    # Time: O(log^2 n)
    # Space: O(log^2 n)
    def min_days(self, n: int) -> int:
        @cache
        def eat(remaining: int) -> int:
            if remaining <= 1:
                return remaining
            by_two = remaining % 2 + 1 + eat(remaining // 2)
            by_three = remaining % 3 + 1 + eat(remaining // 3)
            return min(by_two, by_three)

        return eat(n)