<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>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
class Solution {
public:
    long long merge(vector<int>& nums,int i,int mid ,int j){
        long long ans = 0;
        vector<int> tmp;
        int st = i;
        int k = mid;
        while(st < mid){
            tmp.push_back(nums[st]);
            st++;
        }
        while(k <= j){
            tmp.push_back(nums[k]);
            k++;
        }
        for(int s = mid ; s <= j ; s++){
            int st = i;
            int end = mid-1;
            k = -1;
            while(end >= st){
                int md = (st+end)>>1;
                if(2*1LL*nums[s] < nums[md]){
                 end = md-1;
                 k = md;
                }
                else st = md+1;
            }
            if(k != -1) ans += mid-k;
        }
        sort(tmp.begin(),tmp.end());
        k = 0;
        while(i <= j){
            nums[i] = tmp[k];
            i++;
            k++;
        }
        return ans;
    }
    long long mergeSort(vector<int>& nums,int i, int j){
        if(j == i) return 0;
        int mid = (i+j)>>1;
        long long ans = mergeSort(nums,i,mid)+mergeSort(nums,mid+1,j);
        long long k = merge(nums,i,mid+1,j);
        return ans+k;
    }


    long long reversePairs(vector<int>& nums) {
        // cout << mergeSort(nums,1,nums.size()-1);
        // for(int i : nums) cout << i << " ";
        return mergeSort(nums,0,nums.size()-1);
    }
};
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