<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 merge(self, nums, aux, left, mid, right):
        for k in range(left, right+1):
            aux[k] = nums[k]
        
        inversion_count_per_element = 0 
        
        i, j = left, mid+1
        for k in range(left, right+1):
            if i > mid:
                nums[k] = aux[j]
                j += 1
            elif j > right:
                nums[k] = aux[i]
                nums[k][2] += inversion_count_per_element
                i += 1
            elif aux[i][0] <= aux[j][0]:
                nums[k] = aux[i]
                nums[k][2] += inversion_count_per_element
                i += 1
            else:
                nums[k] = aux[j]
                inversion_count_per_element += 1
                j += 1
    
    def merge_sort(self, nums, aux, left, right):
        if left >= right: return
        
        mid = (left+right)//2
        self.merge_sort(nums, aux, left, mid)
        self.merge_sort(nums, aux, mid+1, right)
        self.merge(nums, aux, left, mid, right)

    def countSmaller(self, nums: List[int]) -> List[int]:
        n = len(nums)
        aux = []
        nums_copy = []
        for index, num in enumerate(nums):
            nums_copy.append([num, index, 0])
            aux.append([num, index, 0])
        self.merge_sort(nums_copy, aux, 0, n-1)
        
        count_smaller = [0]*n
        for item in nums_copy:
            count_smaller[item[1]] = item[2]

        return count_smaller
        

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