<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(nums, res):
            
            if len(nums) > 1:
                m = len(nums) // 2
                left = nums[:m]
                right = nums[m:]
                merge_sort(left, res)
                merge_sort(right, res)
        
                i = 0
                j = 0
                k = 0
                
                inversions = 0
                
                while k < len(left) and j < len(right):
                    if left[k][1] > right[j][1]:
                        nums[i] = right[j]
                        j += 1
                        inversions += 1
                    else:
                        nums[i] = left[k]
                        k += 1
                        res[nums[i][0]] += inversions
                    i += 1

                while k < len(left):
                    nums[i] = left[k]
                    res[nums[i][0]] += inversions
                    k += 1
                    i += 1
                while j < len(right):
                    nums[i] = right[j]
                    i += 1
                    j += 1
                                
        res = defaultdict(int)
        nums = list(enumerate(nums))
        merge_sort(nums, res)
        res = [res.get(i, 0) for i in range(len(nums))]
        return res
        
            
            
            
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