<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:
    SEG = []
    N = 0
    def add_point(self, ind: int, l: int, r: int, pos: int):
        if not r - l == 1:
            if pos < (r + l) // 2:
                self.add_point(2 * ind, l, (r + l) // 2, pos)
            else:
                self.add_point(2 * ind + 1, (r + l) // 2, r, pos)
        self.SEG[ind] += 1
    
    def range_sum(self, ind: int, l: int, r: int, b: int, e: int):
        if l >= b and r <= e:
            return self.SEG[ind]
        if l >= e or r <= b:
            return 0
        return self.range_sum(2 * ind, l, (r + l) // 2, b, e) + self.range_sum(2 * ind + 1, (r + l) // 2, r, b, e)
    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        all_point = set([0])
        sm = 0
        for num in nums:
            sm += num
            all_point.add(sm)
            all_point.add(sm - lower)
            all_point.add(sm - upper)
        all_point = list(all_point)
        all_point = sorted(all_point)
        mp = {}
        sm = 0
        for pt in all_point:
            mp[pt] = sm
            sm += 1
        self.N = len(all_point)
        self.SEG = [0] * (4 * (self.N + 1))
        self.add_point(1, 0, self.N, mp[0])
        res = 0
        sm = 0
        for num in nums:
            sm += num
            res += self.range_sum(1, 0, self.N, mp[sm - upper], mp[sm - lower] + 1)
            self.add_point(1, 0, self.N, mp[sm])
        return res
63383