2171\. Removing Minimum Number of Magic Beans

Medium

You are given an array of **positive** integers `beans`, where each integer represents the number of magic beans found in a particular magic bag.

**Remove** any number of beans (**possibly none**) from each bag such that the number of beans in each remaining **non-empty** bag (still containing **at least one** bean) is **equal**. Once a bean has been removed from a bag, you are **not** allowed to return it to any of the bags.

Return _the **minimum** number of magic beans that you have to remove_.

**Example 1:**

**Input:** beans = [4,**1**,6,5]

**Output:** 4

**Explanation:**

- We remove 1 bean from the bag with only 1 bean.

  This results in the remaining bags: [4,**0**,6,5]
  
- Then we remove 2 beans from the bag with 6 beans.

  This results in the remaining bags: [4,0,**4**,5]

- Then we remove 1 bean from the bag with 5 beans.

  This results in the remaining bags: [4,0,4,**4**]
  
We removed a total of 1 + 2 + 1 = 4 beans to make the remaining non-empty bags have an equal number of beans.

There are no other solutions that remove 4 beans or fewer. 

**Example 2:**

**Input:** beans = [**2**,10,**3**,**2**]

**Output:** 7

**Explanation:**

- We remove 2 beans from one of the bags with 2 beans.

  This results in the remaining bags: [**0**,10,3,2]
  
- Then we remove 2 beans from the other bag with 2 beans.

  This results in the remaining bags: [0,10,3,**0**]
  
- Then we remove 3 beans from the bag with 3 beans.

  This results in the remaining bags: [0,10,**0**,0]
  
We removed a total of 2 + 2 + 3 = 7 beans to make the remaining non-empty bags have an equal number of beans.

There are no other solutions that removes 7 beans or fewer. 

**Constraints:**

*   <code>1 <= beans.length <= 10<sup>5</sup></code>
*   <code>1 <= beans[i] <= 10<sup>5</sup></code>