<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):
        n = len(nums)
        count = [0] * n
        indexes = list(range(n))

        self.merge_sort(nums, indexes, 0, n, count)
        return count

    def merge_sort(self, nums, indexes, left, right, count):
        if right - left <= 1: 
            return

        mid = (left + right) // 2
        self.merge_sort(nums, indexes, left, mid, count)
        self.merge_sort(nums, indexes, mid, right, count)

        self.merge(nums, indexes, left, mid, right, count)

    def merge(self, nums, indexes, left, mid, right, count):
        merged = []
        i, j = left, mid
        right_count = 0  

        while i < mid and j < right:
            if nums[indexes[j]] < nums[indexes[i]]:
                merged.append(indexes[j])
                right_count += 1
                j += 1
            else:
                merged.append(indexes[i])
                count[indexes[i]] += right_count  
                i += 1

        while i < mid:
            merged.append(indexes[i])
            count[indexes[i]] += right_count
            i += 1
        while j < right:
            merged.append(indexes[j])
            j += 1

        for i in range(left, right):
            indexes[i] = merged[i - left]
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