<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, sorted_left, sorted_right):

        i, j = 0,0
        sorted_arr = []
        while i < len(sorted_left) and j < len(sorted_right):

            if sorted_left[i][0] <= sorted_right[j][0]:
                sorted_arr.append(sorted_left[i])
                self.ans[sorted_left[i][1]] += max(len(sorted_arr)-1-i, 0)
                i += 1
            else:
                sorted_arr.append(sorted_right[j])     
                self.ans[sorted_right[j][1]] += max(len(sorted_arr) - len(sorted_left) - j-1, 0)
                j += 1
        
        while i < len(sorted_left):
            sorted_arr.append(sorted_left[i])
            self.ans[sorted_left[i][1]] += max(len(sorted_arr)-1-i, 0)
            i += 1
        
        while j < len(sorted_right):
            sorted_arr.append(sorted_right[j])
            self.ans[sorted_right[j][1]] += max(len(sorted_arr) - len(sorted_left) - j-1, 0)
            j += 1
        
        return sorted_arr

    def merge_sort(self, nums, left, right):
        if left == right:
            return [nums[left]]

        mid = (left + right)//2
        sorted_left = self.merge_sort(nums, left, mid)
        sorted_right = self.merge_sort(nums, mid+1, right)
        sorted_arr = self.merge(sorted_left, sorted_right)

        return sorted_arr

    def countSmaller(self, nums: List[int]) -> List[int]:

        indexed_nums = []
        for i, num in enumerate(nums):
            indexed_nums.append((num, i))
        
        self.ans = [0]*len(nums)
        sorted_arr = self.merge_sort(indexed_nums, 0, len(nums)-1)
        return self.ans
3059