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):  # noqa: E741⏎
        if l == r:  # noqa: E741⏎
            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):  # noqa: E741⏎
        """⏎
        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 l != r:  # noqa: E741⏎
                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:  # noqa: E741⏎
            self.st[idx] = val⏎
            if l != r:  # noqa: E741⏎
                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):  # noqa: E741⏎
        """⏎
        query(1, 1, N, a, b) for query max of [a,b]⏎
        """⏎
        if self.flag[idx] is True:⏎
            self.st[idx] = self.lazy[idx]⏎
            self.flag[idx] = False⏎
            if l != r:  # noqa: E741⏎
                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:  # noqa: E741⏎
            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()⏎