<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 {
public:
    void merge(vector<int>& nums, int low, int mid, int high){
        vector<int> lt;
        int l1=low,l2=mid+1;
        while(l1<=mid && l2<=high){
            if(nums[l1]<nums[l2]){
                lt.push_back(nums[l1++]);
            }
            if(nums[l1]>=nums[l2]){
                lt.push_back(nums[l2++]);
            }
        }
        while(l1<=mid){
            lt.push_back(nums[l1++]);
        }
        while(l2<=high){
            lt.push_back(nums[l2++]);
        }
        for(int i=0;i<lt.size();i++){
            nums[low+i]=lt[i];
        }
    }
    int countPair(vector<int>& arr, int low, int mid, int high){
        int right = mid + 1;
        int cnt = 0;
        for (int i = low; i <= mid; i++) {
            while (right <= high && (long long)arr[i] > (long long)2 * (long long)arr[right]) right++;
            cnt += (right - (mid + 1));
        }
        return cnt;
    }
    int mergeSort(vector<int>& nums,int low,int high){
        int cnt=0;
        if(low>=high) return cnt;
        int mid=(low+high)/2;
        cnt+=mergeSort(nums,low,mid);
        cnt+=mergeSort(nums,mid+1,high);
        cnt+=countPair(nums,low,mid,high);
        merge(nums,low,mid,high);
        return cnt;
    }
    int reversePairs(vector<int>& nums) {
        return mergeSort(nums,0,nums.size()-1);
    }
};
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