<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 SegmentTree:
    def __init__(self, data):
        self.n = len(data)
        self.tree = [0] * (2 * self.n)
        
    def update(self, index, value):
        index += self.n
        self.tree[index] += value
        while index > 1:
            index //= 2
            self.tree[index] = self.tree[2 * index] + self.tree[2 * index + 1]
    
    def query(self, left, right):
        result = 0
        left += self.n
        right += self.n
        while left < right:
            if left % 2:
                result += self.tree[left]
                left += 1
            if right % 2:
                right -= 1
                result += self.tree[right]
            left //= 2
            right //= 2
        return result

class Solution:
    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        prefix_sums = [0]
        for num in nums:
            prefix_sums.append(prefix_sums[-1] + num)
        
        all_sums = sorted(set(prefix_sums + [x - lower for x in prefix_sums] + [x - upper for x in prefix_sums]))
        sum_index = {v: i for i, v in enumerate(all_sums)}
        
        seg_tree = SegmentTree([0] * len(all_sums))
        count = 0
        
        for sum_val in prefix_sums:
            left_index = sum_index[sum_val - upper]
            right_index = sum_index[sum_val - lower]
            count += seg_tree.query(left_index, right_index + 1)
            seg_tree.update(sum_index[sum_val], 1)
        
        return count

60048