<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]:
        output = [0] * len(nums)
        pairs = list(enumerate(nums))

        merge_count(pairs, [None] * len(nums), 0, len(nums) - 1, output)

        return output


def merge_count(nums, temp, start, end, output):
    if start == end:
        return
    
    mid = start + end >> 1
    merge_count(nums, temp, start, mid, output)
    merge_count(nums, temp, mid + 1, end, output)
    
    temp[start : end + 1] = nums[start : end + 1]
    """
        2, 4, 7
        3, 5, 8

        p1
        1, 1, 1
        p2
        1, 1, 1


    """
    p1, p2 = start, mid + 1
    idx = start
    while idx <= end:
        if p2 == end + 1 or p1 < mid + 1 and temp[p1][1] <= temp[p2][1]:
            nums[idx] = temp[p1]
            position = temp[p1][0]
            output[position] += p2 - mid - 1
            p1 += 1

        else:
            nums[idx] = temp[p2]
            p2 += 1
        
        idx += 1




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