import math
from typing import List


class SegmentTree:
    def __init__(self, N: int) -> None:
        self.N = N
        # approximate the overall size of segment tree with array N
        self.st: List[int] = [0 for i in range(0, 4 * N)]
        # create array to store lazy update
        self.lazy: List[int] = [0 for i in range(0, 4 * N)]
        self.flag: List[int] = [0 for i in range(0, 4 * N)]  # flag for lazy update

    def left(self, idx: int) -> int:
        """
        >>> segment_tree = SegmentTree(15)
        >>> segment_tree.left(1)
        2
        >>> segment_tree.left(2)
        4
        >>> segment_tree.left(12)
        24
        """
        return idx * 2

    def right(self, idx: int) -> int:
        """
        >>> segment_tree = SegmentTree(15)
        >>> segment_tree.right(1)
        3
        >>> segment_tree.right(2)
        5
        >>> segment_tree.right(12)
        25
        """
        return idx * 2 + 1

    def build(
        self, idx: int, left_element: int, right_element: int, A: List[int]
    ) -> None:
        if left_element == right_element:
            self.st[idx] = A[left_element - 1]
        else:
            mid = (left_element + right_element) // 2
            self.build(self.left(idx), left_element, mid, A)
            self.build(self.right(idx), mid + 1, right_element, A)
            self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])

    def update(
        self, idx: int, left_element: int, right_element: int, a: int, b: int, val: int
    ) -> bool:
        """
        update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N)
        for each update)

        update(1, 1, N, a, b, v) for update val v to [a,b]
        """
        if self.flag[idx] is True:
            self.st[idx] = self.lazy[idx]
            self.flag[idx] = False
            if left_element != right_element:
                self.lazy[self.left(idx)] = self.lazy[idx]
                self.lazy[self.right(idx)] = self.lazy[idx]
                self.flag[self.left(idx)] = True
                self.flag[self.right(idx)] = True

        if right_element < a or left_element > b:
            return True
        if left_element >= a and right_element <= b:
            self.st[idx] = val
            if left_element != right_element:
                self.lazy[self.left(idx)] = val
                self.lazy[self.right(idx)] = val
                self.flag[self.left(idx)] = True
                self.flag[self.right(idx)] = True
            return True
        mid = (left_element + right_element) // 2
        self.update(self.left(idx), left_element, mid, a, b, val)
        self.update(self.right(idx), mid + 1, right_element, a, b, val)
        self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])
        return True

    # query with O(lg N)
    def query(
        self, idx: int, left_element: int, right_element: int, a: int, b: int
    ) -> int:
        """
        query(1, 1, N, a, b) for query max of [a,b]
        >>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
        >>> segment_tree = SegmentTree(15)
        >>> segment_tree.build(1, 1, 15, A)
        >>> segment_tree.query(1, 1, 15, 4, 6)
        7
        >>> segment_tree.query(1, 1, 15, 7, 11)
        14
        >>> segment_tree.query(1, 1, 15, 7, 12)
        15
        """
        if self.flag[idx] is True:
            self.st[idx] = self.lazy[idx]
            self.flag[idx] = False
            if left_element != right_element:
                self.lazy[self.left(idx)] = self.lazy[idx]
                self.lazy[self.right(idx)] = self.lazy[idx]
                self.flag[self.left(idx)] = True
                self.flag[self.right(idx)] = True
        if right_element < a or left_element > b:
            return -math.inf
        if left_element >= a and right_element <= b:
            return self.st[idx]
        mid = (left_element + right_element) // 2
        q1 = self.query(self.left(idx), left_element, mid, a, b)
        q2 = self.query(self.right(idx), mid + 1, right_element, a, b)
        return max(q1, q2)

    def show_data(self) -> None:
        showList = []
        for i in range(1, N + 1):
            showList += [self.query(1, 1, self.N, i, i)]
        print(showList)


if __name__ == "__main__":
    A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
    N = 15
    segt = SegmentTree(N)
    segt.build(1, 1, N, A)
    print(segt.query(1, 1, N, 4, 6))
    print(segt.query(1, 1, N, 7, 11))
    print(segt.query(1, 1, N, 7, 12))
    segt.update(1, 1, N, 1, 3, 111)
    print(segt.query(1, 1, N, 1, 15))
    segt.update(1, 1, N, 7, 8, 235)
    segt.show_data()