<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]:
        indices = [i for i in range(len(nums))]
        result = [0] * len(nums)

        def helper(l, r):
            if r - l + 1 <= 1:
                return
            
            m = (l + r) // 2
            helper(l, m)
            helper(m + 1, r)
            
            left = indices[l : m + 1]
            right = indices[m + 1 : r + 1]
            i, j, k = 0, 0, l

            count = 0
            while i < len(left) and j < len(right):
                if nums[left[i]] <= nums[right[j]]:
                    result[left[i]] += count
                    indices[k] = left[i]
                    i += 1
                else:
                    count += 1
                    indices[k] = right[j]
                    j += 1
                k += 1
            
            while i < len(left):
                result[left[i]] += count
                indices[k] = left[i]
                i += 1
                k += 1
            while j < len(right):
                indices[k] = right[j]
                j += 1
                k += 1
        
        helper(0, len(nums) - 1)
        return result
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