<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]:
        index = [i for i in range(len(nums))]
        res = [0] * len(nums)

        def mergeSort(arr, start, end):
            if start >= end:
                return
            
            mid = (start + end) // 2
            mergeSort(arr, start, mid)
            mergeSort(arr, mid + 1, end)
            merge(arr, start, mid, end)

        def merge(arr, start, mid, end):
            l1, l2 = start, mid + 1
            temp = []
            count = 0

            while l1 <= mid and l2 <= end:
                if arr[index[l1]] <= arr[index[l2]]:
                    temp.append(index[l1])
                    res[index[l1]] += count
                    l1 += 1
                else:
                    temp.append(index[l2])
                    count += 1
                    l2 += 1
            
            while l1 <= mid:
                temp.append(index[l1])
                res[index[l1]] += count
                l1 += 1
            
            while l2 <= end:
                temp.append(index[l2])
                l2 += 1

            index[start: end + 1] = temp


        mergeSort(nums.copy(), 0, len(nums) - 1)
        return res
        
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