<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]:
#         cache = []
#         res = [0] * len(nums)
#         for i in range(len(nums)-1, -1, -1):
#             idx = bisect.bisect_left(cache, nums[i])
#             res[i] = idx
#             bisect.insort(cache, nums[i])
        
#         return res
        
class TreeNode:
    def __init__(self, value):
        self.value = value
        self.num_left = 0
        self.count = 0
        self.left = None
        self.right = None

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        if not nums:
            return []
        
        vals = sorted(set(nums))
        root = self.construct(vals, 0, len(vals) - 1)

        res = []
        for num in reversed(nums):
            res.append(self.insert(root, num))
        
        return res[::-1]
    
    def insert(self, root, val):
        res = 0
        while root.value != val:
            if val < root.value:
                root.num_left += 1
                root = root.left
            else:
                res += root.count + root.num_left
                root = root.right

        root.count += 1
        return res + root.num_left
    
    def construct(self, vals, left, right):
        if left > right:
            return None
        mid = left + (right - left) // 2
        root = TreeNode(vals[mid])
        root.left = self.construct(vals, left, mid - 1)
        root.right = self.construct(vals, mid + 1, right)

        return root
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