<p>Given an integer array <code>nums</code>, return <em>the number of <strong>reverse pairs</strong> in the array</em>.</p>

<p>A <strong>reverse pair</strong> is a pair <code>(i, j)</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; nums.length</code> and</li>
	<li><code>nums[i] &gt; 2 * nums[j]</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3,2,3,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 3, nums[4] = 1, 3 &gt; 2 * 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,4,3,5,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 4, nums[4] = 1, 4 &gt; 2 * 1
(2, 4) --&gt; nums[2] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 5, nums[4] = 1, 5 &gt; 2 * 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        
#         doubled_nums = [2 * num for num in nums]
        
#         sorted_set = sorted(set(nums).union(set(doubled_nums)))
        
#         rank = 0
#         ranks = {}
        

#         for num in sorted_set:
#             rank += 1
#             ranks[num] = rank
            
#         print(doubled_nums)
#         print(ranks)

#         tree = FenwickTree(len(ranks))

#         reverse_pairs_count = 0
        
#         k = len(doubled_nums) - 1
        
#         for i in range(k, -1, -1):
            
#             # print(reverse_pairs_count)
#             # print(ranks[doubled_nums[i]])
            
#             tree.update(ranks[doubled_nums[i]], 1)
#             reverse_pairs_count += tree.query(ranks[doubled_nums[i] // 2] - 1)
            
#             # print(tree.sums)
            
            
#         return reverse_pairs_count
    
        count = 0
        
        def merge_sort(low, high):
            
            if low == high:
                return
            mid = low + (high - low) // 2
            merge_sort(low, mid)
            merge_sort(mid + 1, high)
            merge(low, mid, high)
            
        def merge(low, mid, high):
            nonlocal count
            i = low
            j = mid + 1
            temp = []
            # while i <= mid and j <= high:
            #     if nums[i] <= 2 * nums[j]:
            #         count += j - (mid + 1)
            #         i += 1
            #     else:
            #         j += 1
            while i <= mid and j <= high:
                if nums[i] > 2 * nums[j]:
                    count += mid - i + 1
                    j += 1
                else:
                    i += 1
            
            i = low
            j = mid + 1   
            while i <= mid and j <= high:
                if nums[i] <= nums[j]:
                    temp.append(nums[i])
                    i += 1
                else:
                    temp.append(nums[j])
                    j += 1

            while i <= mid:
                temp.append(nums[i])
                i += 1
                
            while j <= high:
                temp.append(nums[j])
                j += 1
            i = low
            for each in temp:
                nums[i] = each
                i += 1
        merge_sort(0, len(nums) - 1)
        print(nums)
        return count
            
                
                
        
        
class FenwickTree:
    
    def __init__(self, n):
        self.sums = [0] * (n + 1)
    
    def update(self, i, val):
        while i < len(self.sums):
            self.sums[i] += val
            i += self.getIndex(i)
    
    def query(self, i):
        total = 0
        while i > 0:
            total += self.sums[i]
            i -= self.getIndex(i)
        return total
          
    def getIndex(self, i):
        return i & (-i)


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