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# Minimum Number of Days to Eat N Oranges

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.

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.
```

**Example 3:**

```
Input: n = 1
Output: 1
```

**Example 4:**

```
Input: n = 56
Output: 6
```

**Constraints:**

* `1 <= n <= 2*10^9`

```java
class Solution {
    Map<Integer, Integer> map;

    public int minDays(int n) {
        map = new HashMap<>();
        return helper(n);
    }

    private int helper(int n) {
        if (n <= 1)
            return n;
        if (map.containsKey(n))
            return map.get(n);
        int ans = Integer.MAX_VALUE;
        // 1 -> Divide step, n%2 or n%3 represents the steps of -1
        // to reach the closest multiple or 2 or 3
        ans = Math.min(ans, helper(n / 2) + n % 2 + 1);
        ans = Math.min(ans, helper(n / 3) + n % 3 + 1);
        map.put(n, ans);
        return ans;
    }
}
```