<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]:
        ## merge sort ##
        # 1) initiate 0 list for results and enumerate nums to keep track of idx and value
        # 2) start merge sort algorithm but with both results and enum
        # 3) merge function will contain pointers for left and right arrays,
        # a temp list (which will contain sorted left+right), and a count (# right smaller)
        # 4) while doing the regular merge, append smaller element to temp, add 1 to count if
        # p is bigger, else add count to res for the index
        # 5) also remember to do while p<=mid and while 1<=end
        # 6) replace enum start to end with temp after exiting all while loops
        res = [0 for _ in range(len(nums))]
        enum = list(enumerate(nums))
        def merge_sort(enum, start, end, res):
            if start<end:
                mid = (start+end)//2
                merge_sort(enum, start, mid, res)
                merge_sort(enum, mid+1, end, res)
                merge(enum, start, mid, end, res)
        def merge(enum, start, mid, end, res):
            p, q = start, mid+1
            temp = []
            count = 0
            while p<=mid and q<=end:
                if enum[p][1]>enum[q][1]:
                    count += 1
                    temp.append(enum[q])
                    q += 1
                else:
                    res[enum[p][0]]+=count
                    temp.append(enum[p])
                    p += 1
            while p <= mid: #no more right array
                temp.append(enum[p])
                res[enum[p][0]] += count
                p += 1
            while q <= end:
                temp.append(enum[q])
                q += 1
            enum[start:end+1] = temp
        merge_sort(enum, 0, len(nums)-1, res)
        return res


        
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