### Maximize Greatness of an Array

You are given a 0-indexed integer array `nums`. You are allowed to permute `nums` into a new array `perm` of your choosing.

We define the **greatness** of `nums` be the number of indices `0 <= i < nums.length` for which `perm[i] > nums[i]`.

Return *the **maximum** possible greatness you can achieve after permuting* `nums`.

 

**Example 1:**

```
Input: nums = [1,3,5,2,1,3,1]
Output: 4
Explanation: One of the optimal rearrangements is perm = [2,5,1,3,3,1,1].
At indices = 0, 1, 3, and 4, perm[i] > nums[i]. Hence, we return 4.
```

**Example 2:**

```
Input: nums = [1,2,3,4]
Output: 3
Explanation: We can prove the optimal perm is [2,3,4,1].
At indices = 0, 1, and 2, perm[i] > nums[i]. Hence, we return 3.
```

 

**Constraints:**

- `1 <= nums.length <= 10^5`
- `0 <= nums[i] <= 10^9`


**Function definition**

```
class Solution:
    def maximizeGreatness(self, nums: List[int]) -> int:
```
