<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]:
        nums = nums[::-1]
        nums = list(zip(nums, list(range(len(nums)))))

        res = [0] * len(nums)
        def divide(arr):
            if len(arr) < 2: return arr
            mid = len(arr)//2
            left = divide(arr[:mid])
            right = divide(arr[mid:])
            return merge(left, right)

        def merge(arr1, arr2):
            # print(arr1, arr2)
            if not arr1 or not arr2: return arr1 + arr2
            merge_arr = []
            p1_pointer, p2_pointer = 0, 0
            for p2_pointer in range(len(arr2)):
                while p1_pointer < len(arr1) and arr1[p1_pointer][0] < arr2[p2_pointer][0]:
                    # print("true")
                    p1_pointer += 1
                # print("p1_pointer", p1_pointer)
                res[arr2[p2_pointer][1]] += p1_pointer


            p1, p2 = 0, 0
            while p1 < len(arr1) and p2 < len(arr2):
                if arr2[p2][0] <= arr1[p1][0]:
                    merge_arr.append(arr2[p2])
                    p2 += 1
                else:
                    merge_arr.append(arr1[p1])
                    p1 += 1
            
            merge_arr += arr1[p1:] + arr2[p2:]
            return merge_arr
        divide(nums)
        return res[::-1]

                    
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