<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>

import bisect

class FenwickTree:
    def __init__(self, n: int) -> None:
        self.BIT = [0] * (n+1)
    
    def sum(self, n: int) -> int:
        rv = 0
        while n > 0:
            rv += self.BIT[n]
            n -= n & -n
        return rv
    
    def increment(self, n: int) -> None:
        while n < len(self.BIT):
            self.BIT[n] += 1
            n += n & -n
            
class Solution:
    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        sums = [0] * (len(nums)+1)
        for i, n in enumerate(nums):
            sums[i+1] = sums[i] + n
        sortedSums = sorted(sums)
        ranks = {s: i+1 for i, s in enumerate(sortedSums)}
        ft = FenwickTree(len(sums))
        rv = 0
        for s in sums:
            rv += (ft.sum(bisect.bisect_right(sortedSums, s-lower)) -
                   ft.sum(bisect.bisect_left(sortedSums, s-upper)))
            ft.increment(ranks[s])
        return rv
38371