<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)
        return mergesort(nums, 0, n-1)

def mergesort(nums, low, high):
    cnt = 0
    if low >= high:
        return cnt
    mid = (low + high)//2
    cnt += mergesort(nums, low, mid)
    cnt += mergesort(nums, mid+1, high)
    cnt += countPairs(nums, low, mid, high)
    merge(nums, low, mid, high)
    
    return cnt

def merge(nums, low, mid, high):
    temp = []
    left = low
    right = mid+1

    while(left <= mid and right <= high):
        if nums[left] > nums[right]:
            temp.append(nums[right])
            right += 1
        else:
            temp.append(nums[left])
            left += 1
    while left <= mid:
        temp.append(nums[left])
        left += 1
    while right <= high:
        temp.append(nums[right])
        right += 1

    for i in range(low, high+1):
        nums[i] = temp[i-low]
    return 
def countPairs(nums, low, mid, high):
    cnt = 0
    right = mid+1
    for i in range(low, mid+1):
        while(right<=high and nums[i] > 2*nums[right]):
            right += 1
        cnt += (right - (mid + 1))
    return cnt    
































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































       
24000