<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</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>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        def merge_sort(indices: List[int]) -> List[int]:
            if len(indices) <= 1:
                return indices
            mid = len(indices) // 2
            left = merge_sort(indices[:mid])
            right = merge_sort(indices[mid:])

            merged = []
            i = j = 0
            right_count = 0 

            while i < len(left) and j < len(right):
                if nums[left[i]] > nums[right[j]]:
                    merged.append(right[j])
                    right_count += 1
                    j += 1
                else:
                    merged.append(left[i])
                    counts[left[i]] += right_count
                    i += 1
                
            while i < len(left):
                merged.append(left[i])
                counts[left[i]] += right_count
                i += 1
            while j < len(right):
                merged.append(right[j])
                j += 1
            return merged
        n = len(nums)
        counts = [0] * n
        indices = list(range(n))
        merge_sort(indices)
        return counts





            
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