<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 {
    void merge(vector<int> &nums, int l, int m, int r, int &c) {
        int id = m;

        for(int i=l; i<m; i++) {
            while(id <= r && nums[i] > 2 * 1ll * (nums[id])) id++;
            c += (id - m);
        }

        vector<int> tmp(r - l + 1);
        int i = l, j = m, k = 0;

        while(i < m && j <= r) {
            if(nums[i] < nums[j]) {
                tmp[k++] = nums[i++];
            } else {
                tmp[k++] = nums[j++];
            }
        }

        while(i < m) tmp[k++] = nums[i++];
        while(j <= r) tmp[k++] = nums[j++];

        for(int i=l; i<=r; i++) nums[i] = tmp[i - l];
    }
    int merge_sort(vector<int> &nums, int l, int r) {
        if(l >= r) 
            return 0;
        
        int m = l + (r - l) / 2, c = 0;

        c += merge_sort(nums, l, m);
        c += merge_sort(nums, m+1, r);

        merge(nums, l, m+1, r, c);
        return c;
    }
public:
    int reversePairs(vector<int>& nums) {
        int n = nums.size();
        return merge_sort(nums, 0, n - 1);
    }
};
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