<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 Fenwick:
    def __init__(self, n):
        # print("__init__", n)
        self.T = [0]*(n+1)

    def sum_below(self, e):
        s = 0
        while e > 0:
            s += self.T[e]
            e -= e & (-e)
        return s

    def update(self, i, delta):
        # print("update", i, delta)
        assert i < len(self.T) - 1
        i += 1
        while i < len(self.T):
            self.T[i] += delta
            i += i & (-i)
        

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        smallest = min(nums)
        if smallest < 0:
            for i in range(len(nums)):
                nums[i] += -smallest
        largest = max(nums)
        rfreq = Fenwick(largest+1)

        for n in nums:
            rfreq.update(n, 1)

        counts = []
        for n in nums:
            rfreq.update(n, -1)
            counts.append(rfreq.sum_below(n))
        return counts

    def countSmaller(self, nums: List[int]) -> List[int]:
        smallest = min(nums)
        if smallest < 0:
            for i in range(len(nums)):
                nums[i] += -smallest
        largest = max(nums)
        rfreq = Fenwick(largest+1)

        counts = []
        for i in range(len(nums)-1,-1,-1):
            n = nums[i]
            counts.append(rfreq.sum_below(n))
            rfreq.update(n, 1)
        counts.reverse()
        return counts


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