<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>

class Solution {
public:

    
    long long cnt=0;

    void merge(vector<long long>&suma,int  left,int mid,int right,int lower,int upper){

            vector<long long>tmp(right-left+1,0);
            int k =0;
            int i = left;
            int j = mid+1;

            while(i<=mid && j<=right){
                if(suma[i]>=suma[j]){
                    tmp[k++]=suma[j++];
                }
        
                else{
                    tmp[k++]=suma[i++];
                }

            }

            while(i<=mid){
                tmp[k++]=suma[i++];
            }
            while(j<=right){
                tmp[k++]=suma[j++];
            }
            for(int l=left;l<=right;l++){
                suma[l]=tmp[l-left];
            }

            return;
    }

    void mergesort(vector<long long>&suma,int left,int right,int lower,int upper){


        if(left>=right) return ;

        int mid = left + (right-left)/2;

        mergesort(suma,left,mid,lower,upper);
        mergesort(suma,mid+1,right,lower,upper);


        long long i  = mid+1;
        long long j = mid+1;
        for(int k=left;k<=mid;k++){

            while(i<=right && (suma[i]-suma[k])<=upper) i++;
            while(j<=right && (suma[j]-suma[k])<lower) j++;
            cnt+=(i-j);
        }

        merge(suma,left,mid,right,lower,upper);

        return ;
    }

    int countRangeSum(vector<int>& nums, int lower, int upper) {
        
        int n = nums.size();
        vector<long long>suma(n+1,0);
        for(int i=0;i<n;i++) suma[i+1]=suma[i]+nums[i];

        mergesort(suma,0,n,lower,upper);

        return cnt;
    }
};
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