Mathison has taken a course in Computational Geometry. He managed to solve almost all problems from his latest problem sheet. The hardest one was sent to you and is described below.

You are given a $C \times C$ grid than currently contains no active points and on which you can perform certain operations.
An operation can be an activation $(x, y)$, in which so you mark the point at coordinates $(x, y)$ as active if the point was not already marked. Otherwise, you do nothing.
The second type of operation is a query $(x, y)$ $(x_1, y_1)$ $(x_2, y_2)$: you have to find the greatest manhattan distance between the point $(x, y)$ and any active point that lies inside the rectangle with the bottom-left corner in $(x_1, y_1)$ and the top-right one in $(x_2, y_2)$.

You are given N such operations and you have to execute them all!

Input
The first line of the input file contains one integer, N, representing the number of operations.
Each of the next N lines will contain either an activation or a query in the following format:

• 0 x y: mark the point at $(x, y)$ as active
• 1 x y $x_1$ $y_1$ $x_2$ $y_2$: find the greatest manhattan distance between $(x, y)$ and any active point from $Rectangle((x_1, y_1), (x_2, y_2))$

Output
The output file will contain a line for each operation of type 1. If there is no point in the given rectangle, you should print "no point!" (without quotes).

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le C \le 10^8$
• $0 \le x, y, x_1, y_1, x_2, y_2 \le C$
• $x_1 \le x_2$ and $y_1 \le y_2$ for all rectangles $Rectangle((x_1, y_1), (x_2, y_2))$
• The manhattan distance between A and B is defined to be $d(A, B) = |A_x - B_x| + |A_y - B_y|$.