<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:
    void mergeSort(vector<long long>& psum, int l, int r, const int& lower, const int& upper, long long& ans)
    {
        if (l == r)
        return;
 
        int mid = l + (r - l) / 2;
 
        mergeSort(psum, l, mid, lower, upper, ans);
        mergeSort(psum, mid + 1, r, lower, upper, ans);
 
        int i = l;
        int st = mid + 1;
        int en = mid + 1;
 
        for (;i <= mid; i++)
        {
            while(st <= r && psum[st] - psum[i] < lower)
            st++;
 
            while(en <= r && psum[en] - psum[i] <= upper)
            en++;
 
            ans += en - st;
        }
 
        vector<long long> temp;
        i = l;
        int j = mid + 1;
       
        while(i <= mid && j <= r)
        {
            if (psum[i] <= psum[j])
            {
                temp.push_back(psum[i]);
                i++;
            }
            else
            {
                temp.push_back(psum[j]);
                j++;
            }
        }
 
        while (i <= mid)
        {
            temp.push_back(psum[i]);
            i++;
        }
 
        while(j <= r)
        {
            temp.push_back(psum[j]);
            j++;
        }
 
        for (int itr = l; itr <= r; itr++)
        psum[itr] = temp[itr - l];
    }
 
    int countRangeSum(vector<int>& nums, int lower, int upper) {

        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
 
        int n = nums.size();
 
        vector<long long> psum(n + 1, 0);
 
        for (int i = 0; i < n; i++)
        {
            psum[i + 1] = psum[i] + nums[i];
        }
 
        long long ans = 0;
 
        mergeSort(psum, 0, n, lower, upper, ans);
 
        return ans;
    }
};
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