Problem Statement

There are $N$ pieces on a two-dimensional plane. The coordinates of Piece $i$ are $(X_i,Y_i)$. There may be multiple pieces at the same coordinates.

We will do $M$ operations $\mathrm{op}_1, \ldots, \mathrm{op}_M$, one by one. There are four kinds of operations, described below along with their formats in input.

• 1：Rotate every piece $90$ degrees clockwise about the origin;
• 2：Rotate every piece $90$ degrees counterclockwise about the origin;
• 3 p：Move each piece to the point symmetric to it about the line $x=p$;
• 4 p：Move each piece to the point symmetric to it about the line $y=p$.

You are given $Q$ queries. In the $i$-th query, given two integers $A_i$ and $B_i$, print the coordinates of Piece $B_i$ just after the $A_i$-th operation. Here, the moment just before the $1$-st operation is considered to be the moment just after "the $0$-th operation".

Constraints

• All values in input are integers.
• $1 \leq N \leq 2\times 10^5$
• $1 \leq M \leq 2\times 10^5$
• $1 \leq Q \leq 2\times 10^5$
• $-10^9 \leq X_i,Y_i \leq 10^9$
• $\mathrm{op}_i$ is in the format of one of the four kinds of operations.
• In an operation with the form 3 p or 4 p, $-10^9 \leq p \leq 10^9$.
• $0 \leq A_i \leq M$
• $1 \leq B_i \leq N$

Input

Input is given from Standard Input in the following format:

N
X_1 Y_1
\vdots
X_N Y_N
M
\mathrm{op}_1
\vdots
\mathrm{op}_M
Q
A_1 B_1
\vdots
A_Q B_Q

Output

Print the response to each query in its own line: the $x$- and $y$-coordinates, in this order, with space in between.