Range Module
<p>A Range Module is a module that tracks ranges of numbers. Design a data structure to track the ranges represented as <strong>half-open intervals</strong> and query about them.</p>

<p>A <strong>half-open interval</strong> <code>[left, right)</code> denotes all the real numbers <code>x</code> where <code>left &lt;= x &lt; right</code>.</p>

<p>Implement the <code>RangeModule</code> class:</p>

<ul>
	<li><code>RangeModule()</code> Initializes the object of the data structure.</li>
	<li><code>void addRange(int left, int right)</code> Adds the <strong>half-open interval</strong> <code>[left, right)</code>, tracking every real number in that interval. Adding an interval that partially overlaps with currently tracked numbers should add any numbers in the interval <code>[left, right)</code> that are not already tracked.</li>
	<li><code>boolean queryRange(int left, int right)</code> Returns <code>true</code> if every real number in the interval <code>[left, right)</code> is currently being tracked, and <code>false</code> otherwise.</li>
	<li><code>void removeRange(int left, int right)</code> Stops tracking every real number currently being tracked in the <strong>half-open interval</strong> <code>[left, right)</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;RangeModule&quot;, &quot;addRange&quot;, &quot;removeRange&quot;, &quot;queryRange&quot;, &quot;queryRange&quot;, &quot;queryRange&quot;]
[[], [10, 20], [14, 16], [10, 14], [13, 15], [16, 17]]
<strong>Output</strong>
[null, null, null, true, false, true]

<strong>Explanation</strong>
RangeModule rangeModule = new RangeModule();
rangeModule.addRange(10, 20);
rangeModule.removeRange(14, 16);
rangeModule.queryRange(10, 14); // return True,(Every number in [10, 14) is being tracked)
rangeModule.queryRange(13, 15); // return False,(Numbers like 14, 14.03, 14.17 in [13, 15) are not being tracked)
rangeModule.queryRange(16, 17); // return True, (The number 16 in [16, 17) is still being tracked, despite the remove operation)
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= left &lt; right &lt;= 10<sup>9</sup></code></li>
	<li>At most <code>10<sup>4</sup></code> calls will be made to <code>addRange</code>, <code>queryRange</code>, and <code>removeRange</code>.</li>
</ul>
Design; Segment Tree; Ordered Set
class Node:
    __slots__ = ['left', 'right', 'add', 'v']

    def __init__(self):
        self.left = None
        self.right = None
        self.add = 0
        self.v = False


class SegmentTree:
    __slots__ = ['root']

    def __init__(self):
        self.root = Node()

    def modify(self, left, right, v, l=1, r=int(1e9), node=None):
        if node is None:
            node = self.root
        if l >= left and r <= right:
            if v == 1:
                node.add = 1
                node.v = True
            else:
                node.add = -1
                node.v = False
            return
        self.pushdown(node)
        mid = (l + r) >> 1
        if left <= mid:
            self.modify(left, right, v, l, mid, node.left)
        if right > mid:
            self.modify(left, right, v, mid + 1, r, node.right)
        self.pushup(node)

    def query(self, left, right, l=1, r=int(1e9), node=None):
        if node is None:
            node = self.root
        if l >= left and r <= right:
            return node.v
        self.pushdown(node)
        mid = (l + r) >> 1
        v = True
        if left <= mid:
            v = v and self.query(left, right, l, mid, node.left)
        if right > mid:
            v = v and self.query(left, right, mid + 1, r, node.right)
        return v

    def pushup(self, node):
        node.v = bool(node.left and node.left.v and node.right and node.right.v)

    def pushdown(self, node):
        if node.left is None:
            node.left = Node()
        if node.right is None:
            node.right = Node()
        if node.add:
            node.left.add = node.right.add = node.add
            node.left.v = node.add == 1
            node.right.v = node.add == 1
            node.add = 0


class RangeModule:
    def __init__(self):
        self.tree = SegmentTree()

    def addRange(self, left: int, right: int) -> None:
        self.tree.modify(left, right - 1, 1)

    def queryRange(self, left: int, right: int) -> bool:
        return self.tree.query(left, right - 1)

    def removeRange(self, left: int, right: int) -> None:
        self.tree.modify(left, right - 1, -1)


# Your RangeModule object will be instantiated and called as such:
# obj = RangeModule()
# obj.addRange(left,right)
# param_2 = obj.queryRange(left,right)
# obj.removeRange(left,right)
