<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 sortedcontainers import SortedList

class BIT:
    def __init__(self, n):
        self.arr = [0 for _ in range(n)]

    def get(self, idx):
        total = 0
        while idx != -1:
            total += self.arr[idx]
            idx = (idx & (idx + 1)) - 1
        return total

    def add(self, idx, val):
        while idx < len(self.arr):
            self.arr[idx] += val
            idx = idx | (idx + 1)


class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        n = len(nums)
        permutation = list(range(n))
        permutation.sort(key=lambda idx: (nums[idx], idx))
        # permutation = [3, 2, 1, 4, 0] --> nums[3] < nums[2] < nums[1] < nums[4] < nums[0]
        sorted_nums = [nums[idx] for idx in permutation]

        inv_permutation = [0 for _ in range(n)]
        for idx in range(n):
            inv_permutation[permutation[idx]] = idx
        # inv_permutation[0] is the index of nums[0] in the sorted array

        total = 0
        bit = BIT(n)
        for idx, num in enumerate(nums):
            update_idx = inv_permutation[idx]
            bit_idx = bisect.bisect_right(sorted_nums, 2 * num) - 1
            num_leq = bit.get(bit_idx) if bit_idx >= 0 else 0
            total += idx - num_leq
            bit.add(update_idx, 1)
            
        return total


        # This solution works well, but I am trying to learn Fenwick Trees
        # sl = SortedList()
        # total = 0
        # for num in nums:
        #     total += len(sl) - sl.bisect_right(2 * num)
        #     sl.add(num)
        # return total
28300