<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>

def merge(nums, l, m, h):
    i = l
    j = m+1
    k = 0
    arr = [0 for _ in range(h-l+1)]

    while i<=m and j<=h:
        if nums[i] < nums[j]:
            arr[k] = nums[i]
            i = i + 1
        else:
            arr[k] = nums[j]
            j = j+1
        k= k+1

    while i <=m:
        arr[k] = nums[i]
        i = i + 1
        k = k +1

    while j <=h:
        arr[k] = nums[j]
        j = j + 1
        k = k +1

    for p in range(len(arr)):
        nums[p+l] = arr[p]
    
def count_pairs(a,l,m,h):
    r = m+1
    cnt = 0
    for i in range(l, m+1):
        while r<=h and a[i] > 2* a[r]:
            r = r+1

        cnt = cnt + (r -( m + 1))
    
    return cnt

def merge_sort(nums, l, h):
    cnt = 0
    if l<h:
        m = (l+h) // 2
        cnt = cnt + merge_sort(nums,l,m)
        cnt = cnt + merge_sort(nums, m+1,h)
        cnt = cnt + count_pairs (nums,l,m,h)
        merge(nums, l, m , h)
    return cnt
    
class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        return merge_sort(nums, 0, len(nums) - 1)
        
24000