Count Integers in Intervals
<p>Given an <strong>empty</strong> set of intervals, implement a data structure that can:</p>

<ul>
	<li><strong>Add</strong> an interval to the set of intervals.</li>
	<li><strong>Count</strong> the number of integers that are present in <strong>at least one</strong> interval.</li>
</ul>

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

<ul>
	<li><code>CountIntervals()</code> Initializes the object with an empty set of intervals.</li>
	<li><code>void add(int left, int right)</code> Adds the interval <code>[left, right]</code> to the set of intervals.</li>
	<li><code>int count()</code> Returns the number of integers that are present in <strong>at least one</strong> interval.</li>
</ul>

<p><strong>Note</strong> that an interval <code>[left, right]</code> denotes all the integers <code>x</code> where <code>left &lt;= x &lt;= right</code>.</p>

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

<pre>
<strong>Input</strong>
[&quot;CountIntervals&quot;, &quot;add&quot;, &quot;add&quot;, &quot;count&quot;, &quot;add&quot;, &quot;count&quot;]
[[], [2, 3], [7, 10], [], [5, 8], []]
<strong>Output</strong>
[null, null, null, 6, null, 8]

<strong>Explanation</strong>
CountIntervals countIntervals = new CountIntervals(); // initialize the object with an empty set of intervals. 
countIntervals.add(2, 3);  // add [2, 3] to the set of intervals.
countIntervals.add(7, 10); // add [7, 10] to the set of intervals.
countIntervals.count();    // return 6
                           // the integers 2 and 3 are present in the interval [2, 3].
                           // the integers 7, 8, 9, and 10 are present in the interval [7, 10].
countIntervals.add(5, 8);  // add [5, 8] to the set of intervals.
countIntervals.count();    // return 8
                           // the integers 2 and 3 are present in the interval [2, 3].
                           // the integers 5 and 6 are present in the interval [5, 8].
                           // the integers 7 and 8 are present in the intervals [5, 8] and [7, 10].
                           // the integers 9 and 10 are present in the interval [7, 10].
</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>5</sup></code> calls <strong>in total</strong> will be made to <code>add</code> and <code>count</code>.</li>
	<li>At least <strong>one</strong> call will be made to <code>count</code>.</li>
</ul>
Design; Segment Tree; Ordered Set
class Node:
    __slots__ = ("left", "right", "l", "r", "mid", "v", "add")

    def __init__(self, l, r):
        self.left = None
        self.right = None
        self.l = l
        self.r = r
        self.mid = (l + r) // 2
        self.v = 0
        self.add = 0


class SegmentTree:
    def __init__(self):
        self.root = Node(1, int(1e9) + 1)

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

    def query(self, l, r, node=None):
        if node is None:
            node = self.root
        if l > r:
            return 0
        if node.l >= l and node.r <= r:
            return node.v
        self.pushdown(node)
        v = 0
        if l <= node.mid:
            v += self.query(l, r, node.left)
        if r > node.mid:
            v += self.query(l, r, node.right)
        return v

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

    def pushdown(self, node):
        if node.left is None:
            node.left = Node(node.l, node.mid)
        if node.right is None:
            node.right = Node(node.mid + 1, node.r)
        if node.add != 0:
            left, right = node.left, node.right
            left.add = node.add
            right.add = node.add
            left.v = left.r - left.l + 1
            right.v = right.r - right.l + 1
            node.add = 0


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

    def add(self, left, right):
        self.tree.modify(left, right, 1)

    def count(self):
        return self.tree.query(1, int(1e9))


# Your CountIntervals object will be instantiated and called as such:
# obj = CountIntervals()
# obj.add(left, right)
# param_2 = obj.count()
