<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:
        n = len(nums)

        cntr = 0

        def mergeSort(st, ed):
            if st >= ed:
                return
            
            mid = (st + ed)//2

            mergeSort(st, mid)
            mergeSort(mid + 1, ed)

            # print("-"*50)
            # print(f'sorted 1 [{st}:{mid}] {nums[st:mid+1]}')
            # print(f'sorted 2 [{mid+1}:{ed}] {nums[mid+1:ed+1]}')

            nonlocal cntr
            j = mid + 1
            for i in range(st, mid + 1):
                while j < ed + 1 and nums[i] > 2 * nums[j]:
                    j += 1
                # print(f'{i=} {j=}')
                cntr += (j - (mid + 1))
                # print(f"added {(j - (mid + 1))} {i=} {j=}")
            
            arr1 = nums[st:mid+1] + [float('inf')]
            arr2 = nums[mid+1:ed+1] + [float('inf')]
            n1 = mid + 1 - st
            n2 = ed - mid

            i1, i2 = 0, 0
            i = st

            while i <= ed:
                if arr1[i1] < arr2[i2]:
                    nums[i] = arr1[i1]
                    i1 += 1
                else:
                    nums[i] = arr2[i2]
                    i2 += 1
                i += 1

        mergeSort(0, n-1)

        # print(f"{nums=}")

        return cntr
29400