<p>Given an integer array <code>nums</code>, your goal is to make all elements in <code>nums</code> equal. To complete one operation, follow these steps:</p>

<ol>
	<li>Find the <strong>largest</strong> value in <code>nums</code>. Let its index be <code>i</code> (<strong>0-indexed</strong>) and its value be <code>largest</code>. If there are multiple elements with the largest value, pick the smallest <code>i</code>.</li>
	<li>Find the <strong>next largest</strong> value in <code>nums</code> <strong>strictly smaller</strong> than <code>largest</code>. Let its value be <code>nextLargest</code>.</li>
	<li>Reduce <code>nums[i]</code> to <code>nextLargest</code>.</li>
</ol>

<p>Return <em>the number of operations to make all elements in </em><code>nums</code><em> equal</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,1,3]
<strong>Output:</strong> 3
<strong>Explanation:</strong>&nbsp;It takes 3 operations to make all elements in nums equal:
1. largest = 5 at index 0. nextLargest = 3. Reduce nums[0] to 3. nums = [<u>3</u>,1,3].
2. largest = 3 at index 0. nextLargest = 1. Reduce nums[0] to 1. nums = [<u>1</u>,1,3].
3. largest = 3 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong>&nbsp;All elements in nums are already equal.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,2,2,3]
<strong>Output:</strong> 4
<strong>Explanation:</strong>&nbsp;It takes 4 operations to make all elements in nums equal:
1. largest = 3 at index 4. nextLargest = 2. Reduce nums[4] to 2. nums = [1,1,2,2,<u>2</u>].
2. largest = 2 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>,2,2].
3. largest = 2 at index 3. nextLargest = 1. Reduce nums[3] to 1. nums = [1,1,1,<u>1</u>,2].
4. largest = 2 at index 4. nextLargest = 1. Reduce nums[4] to 1. nums = [1,1,1,1,<u>1</u>].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

from typing import List

class Solution:
    def reductionOperations(self, nums: List[int]) -> int:
        # Sort the array
        nums.sort()
        
        # Initialize variables
        n = len(nums)
        operations = 0
        current_count = 1
        
        # Iterate through the sorted array
        for i in range(n - 1, 0, -1):
            if nums[i] != nums[i - 1]:
                operations += current_count
            current_count += 1
        
        return operations

# Example usage:
solution = Solution()
nums1 = [5, 1, 3]
print(solution.reductionOperations(nums1))  # Output: 3

nums2 = [1, 1, 1]
print(solution.reductionOperations(nums2))  # Output: 0

nums3 = [1, 1, 2, 2, 3]
print(solution.reductionOperations(nums3))  # Output: 4
740