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".

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.

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 $4 p, -10^9 \leq p \leq 10^9$.
• $0 \leq A_i \leq M$
• $1 \leq B_i \leq N$

Sample Input 1

1
1 2
4
1
3 3
2
4 2
5
0 1
1 1
2 1
3 1
4 1

Sample Output 1

1 2
2 -1
4 -1
1 4
1 0

Initially, the only piece - Piece 1 - is at (1, 2). Each operation moves the piece as follows: $(1,2)\to(2,-1)\to(4,-1)\to(1,4)\to(1,0)$.

Sample Input 2

2
1000000000 0
0 1000000000
4
3 -1000000000
4 -1000000000
3 1000000000
4 1000000000
2
4 1
4 2

Sample Output 2

5000000000 4000000000
4000000000 5000000000

见题面 Input 部分

见题面 Output 部分