<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>

// Segment tree Sum
class ST {
    int64_t n;
    vector<int64_t> tree;
public:
    ST(const vector<int64_t>& data) {
        int64_t N = data.size();
        n = N;
        tree.resize(2 * n);
        for (int64_t i = 0; i < n; i++) {
            tree[i + n] = data[i];
        }
        build();
    }

    void build() {  // build the tree
        for (int64_t i = n - 1; i > 0; --i) tree[i] = tree[i<<1] + tree[i<<1|1];
    }

    void modify(int64_t p) {  // set value at position p
        for (tree[p += n] += 1; p > 1; p >>= 1) tree[p>>1] = tree[p] + tree[p^1];
    }

    int64_t query(int64_t l, int64_t r) {  // sum on interval [l, r]
        r++;
        int64_t res = 0;
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l&1) res += tree[l++];
            if (r&1) res += tree[--r];
        }
        return res;
    }
};

class Solution {
public:
    int64_t reversePairs(vector<int>& a) {
        int64_t n = a.size();
        vector<int64_t> data(n, 0);

        vector<int> b = a;
        sort(b.begin(), b.end());
        function<int64_t(int64_t)> get = [&](int64_t val) {
            return upper_bound(b.begin(), b.end(), val) - b.begin();
        };

        ST st(data);
        int64_t ans = 0;
        for (auto e : a) {
            int64_t key = get(2 * (int64_t)e);
            if (key != n) {
                int64_t cnt = st.query(key, n - 1);
                ans += cnt;
            }  
            st.modify(get(e) - 1);
        }
        return ans;
    }
};
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