<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):
        def mergeSort(start, end):
            if end - start <= 1:
                return
            mid = (start + end) // 2
            mergeSort(start, mid)
            mergeSort(mid, end)
            merge(start, mid, end)

        def merge(start, mid, end):
            left = indices[start:mid]
            right = indices[mid:end]
            i = j = 0
            while i < len(left) and j < len(right):
                if nums[left[i]] > nums[right[j]]:
                    # Since nums[left[i]] is greater, it means all elements in the right array
                    # from right[j] onward are smaller than nums[left[i]]
                    counts[left[i]] += len(right) - j
                    indices[start] = left[i]
                    i += 1
                else:
                    indices[start] = right[j]
                    j += 1
                start += 1
            # If there are remaining elements in the left array, append them
            while i < len(left):
                indices[start] = left[i]
                i += 1
                start += 1
            # If there are remaining elements in the right array, append them
            while j < len(right):
                indices[start] = right[j]
                j += 1
                start += 1

        n = len(nums)
        counts = [0] * n
        indices = list(range(n))
        mergeSort(0, n)
        return counts


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