<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 mergesort(nums: List[Tuple[int, int, int]]) -> List[Tuple[int, int, int]]:
            if len(nums) <= 1:
                return nums
            middle = len(nums) // 2
            left_sorted = mergesort(nums[:middle])
            right_sorted = mergesort(nums[middle:])
            return merge(left_sorted, right_sorted)
    
        def merge(
            left: List[Tuple[int, int, int]], right: List[Tuple[int, int, int]]
        ) -> List[Tuple[int, int, int]]:
            res = []
            i, j = 0, 0
    
            while i < len(left) and j < len(right):
                if left[i][0] <= right[j][0]:
                    left[i] = (left[i][0], left[i][1], left[i][2] + j)
                    res.append(left[i])
                    i += 1
                else:
                    res.append(right[j])
                    j += 1
    
            # res.extend(left[i:])
            for i in range(i, len(left)):
                left[i] = (left[i][0], left[i][1], left[i][2] + j)
                res.append(left[i])
    
            res.extend(right[j:])
            return res
    
        enumerated = [(val, ind, 0) for (ind, val) in enumerate(nums)]
        sorted_nums = mergesort(enumerated)
        res = [0] * len(nums)
        for val in sorted_nums:
            res[val[1]] = val[2]
    
        return res

2012