<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:
    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        pre = [0]*(len(nums)+1)
        for i in range(1,len(nums)+1):
            pre[i] = pre[i-1] + nums[i-1]

        for i in pre:
            print(i," ",end="")
    
        self.ans = 0

        def merge(l,mid,h):

            start,end = mid+1 , mid+1

            for i in range(l,mid+1):
                while start <= h and pre[start] - pre[i] < lower :
                    start += 1
                while end <= h and pre[end] - pre[i] <= upper:
                    end+=1
                self.ans += (end-start)

            s = []
            i,j = l,mid+1
            while i <= mid and j <= h :
                if pre[i] < pre[j]:
                    s.append(pre[i])
                    i += 1
                else:
                    s.append(pre[j])
                    j+= 1
            s += pre[i:mid+1] + pre[j:h+1]
            for i in range(len(s)):
                pre[i+l] = s[i]
    


        def sort(l,h):
            if l < h :
                mid = l + (h-l)//2 
                sort(l,mid)
                sort(mid+1,h)
                merge(l,mid,h)

        
        sort(0,len(nums))

        print()
        for i in pre:
            print( i , " ",end ="" )

        return self.ans

        
        
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