<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:
        def merge(left, right):
            sorted_arr = []

            l, r = 0, 0

            while l < len(left) and r < len(right):
                if left[l] < right[r]:
                    sorted_arr.append(left[l])
                    l += 1
                else:
                    sorted_arr.append(right[r])
                    r += 1

            while l < len(left):
                sorted_arr.append(left[l])
                l += 1

            while r < len(right):
                sorted_arr.append(right[r])
                r += 1

            return sorted_arr

        def dnc(arr):
            if len(arr) == 1:
                return arr, 0

            m = len(arr) // 2

            left_sorted, left_invs = dnc(arr[:m])
            right_sorted, right_invs = dnc(arr[m:])

            total_invs = 0
            l, r = 0, 0

            while l < len(left_sorted) and r < len(right_sorted):
                if left_sorted[l] > 2 * right_sorted[r]:
                    total_invs += len(left_sorted) - l
                    r += 1
                else:
                    l += 1

            arr_sorted = merge(left_sorted, right_sorted)

            return arr_sorted, total_invs + left_invs + right_invs

        return dnc(nums)[1]

24400