<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>

#define ll long long

class BIT {
    public:

    vector<int> tree;

    BIT(int n) {
        tree.resize(n, 0);
    }

    int getSum(int ind) {
        int sum = 0;
        while ( ind > 0 ) {
            sum += tree[ind];
            ind -= (ind & -ind);
        }
        return sum;
    }

    void update(int ind, int val) {
        while ( ind < tree.size() ) {
            tree[ind] += val;
            ind += (ind & -ind);
        }
    }

    int getRightSum(int ind) {
        return getSum(tree.size() - 1) - getSum(ind);
    }

};

class Solution {
public:
    int reversePairs(vector<int>& nums) {
        int ind = 1, n = nums.size();
        unordered_map<int, int> mp;
        vector<int> sortedNums = nums;
        sort(sortedNums.begin(), sortedNums.end());

        for ( auto num: sortedNums ) {
            if ( mp[num] == 0 ) mp[num] = ind++;
        }

        BIT Bit(ind);
        int ans = 0;
        for ( int i = 0; i < n; i++ ) {
            int j = upper_bound(
                sortedNums.begin(), 
                sortedNums.end(), 
                2ll * nums[i]
            ) - sortedNums.begin();

            if ( j < n ) {
                ans += Bit.getRightSum(mp[sortedNums[j]] - 1);
            }

            Bit.update(mp[nums[i]], 1);
        }
        return ans;
    }
};
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