<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>

from bisect import bisect_right
class BIT:
    def __init__(self, n):
        self.len = n+1
        self.sum = [0] * self.len

    def search(self, x):
        res = 0
        while(x > 0):
            res += self.sum[x]
            x = x - (x & -x)
        return res
    
    def insert(self, x, delta):
        while(x < self.len):
            self.sum[x] += delta
            x = x + (x & -x)
        
class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        sorted_nums = sorted(set(nums))
        bit = BIT(len(sorted_nums))
        rank = {}
        for i, n in enumerate(sorted_nums):
            rank[n] = i+1
        
        res = 0
        for i, n in enumerate(nums):
            res += i - bit.search(bisect_right(sorted_nums, n*2))
            bit.insert(rank[n], 1)
        return res
   

        
27400