<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]:
        class Pairs:
            def __init__(self,val,id):
                self.val=val
                self.id=id
        self.temp=[Pairs(0,0) for i in range(len(nums))]
        self.count=[0 for i in range(len(nums))]
        def merge(nums,left,mid,right):
            for i in range(left,right+1):
                self.temp[i]=nums[i]
            m,n,p=left,mid+1,left
            while p<=right:
                if m==mid+1:
                    nums[p]=self.temp[n]
                    n+=1
                elif n==right+1:
                    nums[p]=self.temp[m]
                    m+=1
                    self.count[nums[p].id]+=n-mid-1
                elif self.temp[m].val>self.temp[n].val:
                    nums[p]=self.temp[n]
                    n+=1
                elif self.temp[m].val<=self.temp[n].val:
                    nums[p]=self.temp[m]
                    m+=1
                    self.count[nums[p].id]+=n-mid-1
                p+=1

        def sort(nums,left,right):
            if left==right: return nums
            mid=left+(right-left)//2
            sort(nums,left,mid)
            sort(nums,mid+1,right)
            merge(nums,left,mid,right)
        
        arr=[Pairs(nums[i],i) for i in range(len(nums))]
        sort(arr,0,len(nums)-1)
        res=[c for c in self.count]
        return res

        
        
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