Vector Calculator

Listen up soldier! You are going into the front lines, maggot! I don't wanna hear about "integers" or "real numbers anymore". Drop and give me twenty, and then implement a calculator that can calculate 2d vector operations!!!!!!.

Input format

The first line has one integer, ~n~, the number of queries.

~n~ lines follow, each with a query.

There are 3 query types with vector outputs.

Add queries are in format "~ADD~ ~a_x~ ~a_y~ ~b_x~ ~b_y~". The answer to this query is the sum of vectors ~(a_x, a_y)~ and ~(b_x, b_y)~

Multiplication queries are in format "~MULT~ ~a_x~ ~a_y~ ~b~". The answer to this query is the multiplication of vector ~(a_x, a_y)~ and the scalar ~b~

Rotation queries are in format "~ROT~ ~a_x~ ~a_y~ ~ang~". The answer to this query is the resulting vector after rotating vector ~(a_x, a_y)~ around the origin by ~ang~ degrees counterclockwise

There are 3 queries with scalar outputs.

Triangle queries are in format "~TRI~ ~a_x~ ~a_y~ ~b_x~ ~b_y~ ~c_x~ ~c_y~". The answer to this query is area of the triangle with points ~(a_x,a_y)~, ~(b_x,b_y)~ and ~(c_x,c_y)~

Dot product queries are in format "~DOT~ ~a_x~ ~a_y~ ~b_x~ ~b_y~". The answer to this query is the dot product of vectors ~(a_x, a_y)~ and ~(b_x, b_y)~

Cross product queries are in format "~CROSS~ ~a_x~ ~a_y~ ~b_x~ ~b_y~". The answer to this query is the cross product of vectors ~(a_x, a_y)~ and ~(b_x, b_y)~

~1 < n < 1e5~

All numbers in queries are in range ~[-1e5, 1e5]~

Output format

For each query, output the answer on a separate line. For vector outputs, print out the answer in format "~x~ ~y~", where ~x~ is the horizontal component, and ~y~ is the vertical component For scalar outputs, simply print out the answer in a separate line.

Tip: be careful of the print format, we don't the program to print in scientific form, or to be skimping out on decimal places. For c++ users, ~cout << setPrecision(10)~, imported from the iomanip library can resolve this.

Answers within 1e-5 of the reference answer will be accepted.

Examples

Input

3
ADD 3.5 4.5 6 -3
ROT 1 4.5 90
MULT -3892 3 0.5

Output

9.5 1.5
-4.5 1
-1946 1.5

Input

2
TRI 0 0 1 0 0 1
DOT 3000 4000 4000 -3000

Output

0.5
0

Input

1
CROSS -3.5 -6.5 7 13

Output

0