<p>You are given a 0-indexed integer array <code>nums</code>. You are allowed to permute <code>nums</code> into a new array <code>perm</code> of your choosing.</p>

<p>We define the <strong>greatness</strong> of <code>nums</code> be the number of indices <code>0 &lt;= i &lt; nums.length</code> for which <code>perm[i] &gt; nums[i]</code>.</p>

<p>Return <em>the <strong>maximum</strong> possible greatness you can achieve after permuting</em> <code>nums</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,3,5,2,1,3,1]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One of the optimal rearrangements is perm = [2,5,1,3,3,1,1].
At indices = 0, 1, 3, and 4, perm[i] &gt; nums[i]. Hence, we return 4.</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can prove the optimal perm is [2,3,4,1].
At indices = 0, 1, and 2, perm[i] &gt; nums[i]. Hence, we return 3.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def maximizeGreatness(self, nums: List[int]) -> int:
        # sort the array
        # count the numbers
        # iterate through the sorted array
        # find the next biggest number
        # if the counter is bigger than 0, decrement the counter, increment the result
        # return the result
        nums.sort()
        freq = defaultdict(int)
        for v in nums:
            freq[v] += 1
        result, m = 0, 1
        for i in range(len(nums)):
            for j in range(m, len(nums)):
                if nums[j] > nums[i] and freq[nums[j]] > 0:
                    result += 1
                    freq[nums[j]] -= 1
                    m = j
                    break
        return result



'''
[42,8,75,28,35,21,13,21]

[8, 13, 21, 21, 28, 35, 42, 75]
13, 21, 28, 35, 42, 75

'''
33800