<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(object):
    
    def find_positions(self, nums, i, j, val) :
        if val <= nums[0] :
            return 0
        if val > nums[-1] :
            return len(nums)
        # if j == i + 1 :
        #     if val > nums[i] and val <= nums[j] :
        #         return i + 1
        #     if val 
        mid = (i+j)/2
        if val > nums[mid] and val <= nums[mid+1] :
            return mid + 1
        if val > nums[mid] :
            return self.find_positions(nums, mid, j, val)
        return self.find_positions(nums, i, mid, val)
    
    def countSmaller(self, nums):
        """
        :type nums: List[int]
        :rtype: List[int]
        """
        
        if len(nums) == 0 :
            return []
        
        if len(nums) == 1 :
            return [0]
        
#         new_arr = [nums[-1]]
#         ans = [0]
#         l = len(nums)
#         for i in reversed(range(l-1)) :
#             pos = self.find_positions(new_arr, 0, len(new_arr)-1, nums[i])
#             ans.append(pos)
#             new_arr = new_arr[:pos] + [nums[i]] + new_arr[pos:]
        
#         return ans[::-1]
        def sort(enums) :
            if len(enums) == 1 :
                return enums
            l = len(enums)
            left, right = sort(enums[0:l//2]), sort(enums[l//2:])
            temp = []
            i = len(left) - 1
            j = len(right) - 1
            while i >=0  and j >= 0  :
                if left[i][1] > right[j][1] :
                    temp.append(left[i])
                    smaller[left[i][0]] += j + 1
                    i -= 1
                else :
                    temp.append(right[j])
                    j -= 1
                
            while i >= 0 :
                temp.append(left[i])
                i -= 1
            
            while j >= 0 :
                temp.append(right[j])
                j -= 1
            return temp[::-1]
        
            
        smaller = [0] * len(nums)
        out = sort(list(enumerate(nums)))
        print(out)
        return smaller
    
        
                        
            
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