<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 _get_count(left, right, counts):
            if left >= right:
                return counts

            # Count
            mid = left + (right - left) // 2
            _get_count(left, mid, counts)
            _get_count(mid + 1, right, counts)

            right_i = mid + 1
            for left_i in range(left, mid + 1):
                while right_i <= right and nums[left_i][0] > nums[right_i][0]:
                    right_i += 1
                counts[nums[left_i][1]] += right_i - (mid + 1)

            # Merge
            merged = [None] * (right - left + 1)
            merged_i, left_i, right_i = 0, left, mid + 1
            while left_i < mid + 1 and right_i < right + 1:
                if nums[left_i][0] < nums[right_i][0]:
                    merged[merged_i] = nums[left_i]
                    left_i += 1
                else:
                    merged[merged_i] = nums[right_i]
                    right_i += 1
                merged_i += 1
            while left_i < mid + 1:
                merged[merged_i] = nums[left_i]
                left_i += 1
                merged_i += 1
            while right_i < right + 1:
                merged[merged_i] = nums[right_i]
                right_i += 1
                merged_i += 1

            for i in range(len(merged)):
                nums[left] = merged[i]
                left += 1

            return counts

        n = len(nums)
        nums = [[num, i] for i, num in enumerate(nums)]
        return _get_count(0, n - 1, [0] * n)

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