import math


class SegmentTree:
    def __init__(self, N):
        self.N = N
        self.st = [
            0 for i in range(0, 4 * N)
        ]  # approximate the overall size of segment tree with array N
        self.lazy = [0 for i in range(0, 4 * N)]  # create array to store lazy update
        self.flag = [0 for i in range(0, 4 * N)]  # flag for lazy update

    def left(self, idx):
        return idx * 2

    def right(self, idx):
        return idx * 2 + 1

    def build(self, idx, l, r, A):
        if l == r:
            self.st[idx] = A[l - 1]
        else:
            mid = (l + r) // 2
            self.build(self.left(idx), l, mid, A)
            self.build(self.right(idx), mid + 1, r, A)
            self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])

    # update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N) for each update)
    def update(
        self, idx, l, r, a, b, val
    ):  # update(1, 1, N, a, b, v) for update val v to [a,b]
        if self.flag[idx] == True:
            self.st[idx] = self.lazy[idx]
            self.flag[idx] = False
            if l != r:
                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 r < a or l > b:
            return True
        if l >= a and r <= b:
            self.st[idx] = val
            if l != r:
                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 = (l + r) // 2
        self.update(self.left(idx), l, mid, a, b, val)
        self.update(self.right(idx), mid + 1, r, 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, l, r, a, b):  # query(1, 1, N, a, b) for query max of [a,b]
        if self.flag[idx] == True:
            self.st[idx] = self.lazy[idx]
            self.flag[idx] = False
            if l != r:
                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 r < a or l > b:
            return -math.inf
        if l >= a and r <= b:
            return self.st[idx]
        mid = (l + r) // 2
        q1 = self.query(self.left(idx), l, mid, a, b)
        q2 = self.query(self.right(idx), mid + 1, r, a, b)
        return max(q1, q2)

    def showData(self):
        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.showData()