7808: [CSES Problem Set] Point Location Test
[Creator : ]
Description
There is a line that goes through the points $p_1=(x_1,y_1)$ and $p_2=(x_2,y_2)$. There is also a point $p_3=(x_3,y_3)$.
Your task is to determine whether $p_3$ is located on the left or right side of the line or if it touches the line when we are looking from $p_1$ to $p_2$.
Your task is to determine whether $p_3$ is located on the left or right side of the line or if it touches the line when we are looking from $p_1$ to $p_2$.
Input
The first input line has an integer $t$: the number of tests.
After this, there are $t$ lines that describe the tests. Each line has six integers: $x_1, y_1, x_2, y_2, x_3, y_3$.
After this, there are $t$ lines that describe the tests. Each line has six integers: $x_1, y_1, x_2, y_2, x_3, y_3$.
Output
For each test, print "LEFT", "RIGHT" or "TOUCH".
Constraints
$1≤t≤10^5$
$-10^9≤x_1,y_1,x_2,y_2,x_3,y_3≤10^9$
$x_1 \neq x_2$ or $y_1≠y_2$
$-10^9≤x_1,y_1,x_2,y_2,x_3,y_3≤10^9$
$x_1 \neq x_2$ or $y_1≠y_2$
Sample 1 Input
3
1 1 5 3 2 3
1 1 5 3 4 1
1 1 5 3 3 2
Sample 1 Output
LEFT
RIGHT
TOUCH