<p>Given an integer array <code>nums</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of range sums that lie in</em> <code>[lower, upper]</code> <em>inclusive</em>.</p>

<p>Range sum <code>S(i, j)</code> is defined as the sum of the elements in <code>nums</code> between indices <code>i</code> and <code>j</code> inclusive, where <code>i &lt;= j</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [-2,5,-1], lower = -2, upper = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0], lower = 0, upper = 0
<strong>Output:</strong> 1
</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>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

// Using the pbds for the solution
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// #define ll long long
// typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
// typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_multiset;
// typedef tree<pair<ll, ll>, null_type, less<pair<ll, ll>>, rb_tree_tag, tree_order_statistics_node_update> ordered_pair_set;

#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;
#define ll long long
typedef tree<ll,null_type,less<ll>,rb_tree_tag, tree_order_statistics_node_update> ordered_set;
typedef tree<pair<ll,ll>,null_type,less<pair<ll,ll>>,rb_tree_tag, tree_order_statistics_node_update> ordered_pair_set;


// order_of_key(val)  --> number pf elem less than val
class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        // ordered pair set use krenge instead of multiset
        ordered_pair_set st;

        ll n=nums.size();
        ll sum=0;
        ll ans=0;
        st.insert({0,-1});
        for(int i=0;i<n;i++){
            sum+=nums[i];

            ll l=sum-upper,r=sum-lower;
            // we have to find the number of prefix sum before this which is in range [l,r]
            ll ct=st.order_of_key({r+1,-5})-st.order_of_key({l,-5});
            ans+=ct;

            st.insert({sum,i});
        }

        return ans;
    }
};
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