<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]:
        ans = [0] * len(nums)
        arr = [[v, i] for i, v in enumerate(nums)]

        def mergeSort(arr):
            if len(arr) <= 1:
                return arr

            mid = len(arr) // 2
            leftHalf = arr[:mid]
            rightHalf = arr[mid:]

            sortedLeft = mergeSort(leftHalf)
            sortedRight = mergeSort(rightHalf)

            return merge(sortedLeft, sortedRight)

        def merge(left, right):
            result = []
            i = j = 0

            while i < len(left) and j < len(right):
                if left[i][0] <= right[j][0]:
                    result.append(left[i])
                    ans[left[i][1]] += j
                    i += 1
                else:
                    result.append(right[j])
                    j += 1

            while i < len(left):
                result.append(left[i])
                ans[left[i][1]] += j
                i += 1
            result.extend(right[j:])

            return result

        mergeSort(arr)
        return ans
1785