<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:
        res = 0
        temp = [0] * len(nums)

        # [left, right]
        def sort(left, right):
            if left == right:
                return

            mid = left + ((right-left) // 2)
            sort(left, mid)
            sort(mid+1, right)
            merge(left, mid, right)
        
        # mid is the last element in first partition
        def merge(left, mid, right):
            nonlocal res
            for i in range(left, right+1):
                temp[i] = nums[i]

            # find count
            rightbound = mid+1
            for i in range(left, mid+1):
                # find first num in right part that is > 2 * nums[j]
                # [7] [2,3,4]
                while rightbound <= right and nums[i] > 2*nums[rightbound]:
                    rightbound += 1
                
                res += rightbound - (mid+1)

            # merge
            l = left
            r = mid + 1
            for i in range(left, right+1):
                if r == right+1:
                    nums[i] = temp[l]
                    l += 1
                elif l == mid+1:
                    nums[i] = temp[r]
                    r += 1
                elif temp[l] > temp[r]:
                    nums[i] = temp[r]
                    r += 1
                else:
                    nums[i] = temp[l]
                    l += 1

        sort(0, len(nums)-1)

        return res
31800