<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class SegmentTree{
    vector<int> tree;
    int n;
public:
    SegmentTree(int _n){
        n = _n;
        tree.resize(4*n, 0);
    }
    
    int query(int x, int y, int l, int r, int i){
        if(r < x || y < l) return 0;
        if(x <= l && r <= y) return tree[i];

        int m = (l+r)/2;
        return query(x, y, l, m, 2*i+1) + query(x, y, m+1, r, 2*i+2);
    }

    void update(int ind, int val, int l, int r, int i){
        if(l == r){
            tree[i] = val;
            return;
        }

        int m = (l+r)/2;
        if(ind <= m) update(ind, val, l, m, 2*i+1);
        else update(ind, val, m+1, r, 2*i+2);

        tree[i] = tree[2*i+1] + tree[2*i+2];
    }
};

class Solution {
public:
    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector<pair<int,int>> arr;
        for(int i = 0; i < n; i++){
            arr.push_back({nums[i], i});
        }

        sort(arr.begin(), arr.end());

        map<pair<int, int>, int> mp;
        for(int i = 0; i < n; i++){
            mp[arr[i]] = i;
        }

        vector<int> ans(n, 0);
        SegmentTree tree(n+1);

        for(int i = n-1; i >= 0; i--){
            int ind = mp[{nums[i], i}];
            ans[i] = tree.query(0, ind-1, 0, n-1, 0);

            tree.update(ind, 1, 0, n-1, 0);
        }

        return ans;
    }
};
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