<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:
    bit=[]
    def getRSB(self, i):
        return i & -i
    def getSum(self, i):
        s = 0
        while i > 0:
            s += self.bit[i]
            i -= self.getRSB(i)
        return s
    
    def update(self, i):
        while i < len(self.bit):
            self.bit[i] += 1
            i += self.getRSB(i)

    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        n = len(nums)
        psum = [0 for i in range(n+1)]
        for i in range(n):
            psum[i+1] = psum[i] + nums[i]
        
        sorted_psum = sorted(psum)
        sorted_psum_map = {val: idx for idx, val in enumerate(sorted_psum)}

        res = 0
        self.bit = [0 for i in range(n+2)]

        print(sorted_psum)

        for i in range(n+1):
            pleft = psum[i] - upper
            pright = psum[i] - lower
            x = bisect.bisect_left(sorted_psum, pleft)
            y = bisect.bisect_right(sorted_psum, pright)

            lsum = self.getSum(x)
            rsum = self.getSum(y)

            res += rsum - lsum

            index = sorted_psum_map[psum[i]]
            self.update(index+1)

        return res


            
        
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