<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:

    int helper(vector<int>& nums, int lower, int upper, int start, int end) {
        int n = nums.size();
        if(start == end){
            if(nums[start] >= lower && nums[end] >= upper)return(1);
            else return(0);
        }
        else if(start > end)return(0);

        int mid = (start + end)/2;
        int x = helper(nums, lower, upper, start, mid);
        int y = helper(nums, lower, upper, mid+1, end);
        int cur = 0;
        int s = nums[mid] + nums[mid+1];

        return(x + y + cur);
    }

    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int ans = 0;
        int n = nums.size();
        vector<pair<long long int, int>> pre, suf;
        long long int s = 0;
        for(int i=0;i<n;i++){
            s += nums[i];
            if(s >= lower && s<=upper)ans++;
            pre.push_back({s, i});
        }
        s = 0;
        for(int i=n-1;i>=0;i--){
            s += nums[i];
            if(s >= lower && s<=upper && i!=0)ans++;
            suf.push_back({s,i});
        }
        sort(pre.begin(), pre.end());
        sort(suf.begin(), suf.end());
        // for(auto &c:pre)cout << "(" << c.first << " ," << c.second << ") ";cout<<endl;
        // for(auto &c:suf)cout << "(" << c.first << " ," << c.second << ") ";cout<<endl;

        for(int i=0;i<n;i++){
            int x = pre[i].first;
            int y = pre[i].second;
            long long int up = s-x-lower;
            long long int low = s-x-upper;
            int k = lower_bound(suf.begin(), suf.end(), make_pair(low, -1)) - suf.begin();
            for(int j=k;j<n;j++){
                if(suf[j].first > up)break;
                if(suf[j].second < y+2)continue;
                else ans++;
            }
        }
        return(ans);


    }
};
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