<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(arr, indices):
            if len(arr) <= 1:
                return arr, indices
            
            mid = len(arr) // 2
            left, left_indices = merge_sort(arr[:mid], indices[:mid])
            right, right_indices = merge_sort(arr[mid:], indices[mid:])
            
            merged = []
            merged_indices = []
            i = j = 0
            while i < len(left) or j < len(right):
                if j == len(right) or (i < len(left) and left[i] <= right[j]):
                    counts[left_indices[i]] += j
                    merged.append(left[i])
                    merged_indices.append(left_indices[i])
                    i += 1
                else:
                    merged.append(right[j])
                    merged_indices.append(right_indices[j])
                    j += 1
            
            return merged, merged_indices
        
        n = len(nums)
        counts = [0] * n
        indices = list(range(n))
        merge_sort(nums, indices)
        return counts
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