Vector Calculator

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

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

9.5 1.5
-4.5 1
-1946 1.5

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

0.5
0

1
CROSS -3.5 -6.5 7 13

0