<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>

from collections import deque

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        res = [0] * len(nums)
        enum = list(enumerate(nums))

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

    
    def mergeSort(self, enum, res, low, high):
        if low < high:
            mid = (low + high) // 2
            left = self.mergeSort(enum, res, low, mid)
            right = self.mergeSort(enum, res, mid + 1, high)

            p, q = low, mid + 1
            temp = []
            count = 0

            while p <= mid and q <= high:
                if enum[p][1] <= enum[q][1]:
                    temp.append(enum[p])
                    res[enum[p][0]] += count
                    p += 1
                else:
                    temp.append(enum[q])
                    count += 1
                    q += 1
            
            while p <= mid:
                temp.append(enum[p])
                res[enum[p][0]] += count
                p += 1
            
            while q <= high:
                temp.append(enum[q])
                q += 1

            enum[low: high + 1] = temp
        
        else:
            return
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