Crocodile Hunting
It is well-known that crocodiles are not the friendliest of creatures. But what happens when they live in a zoo and require care? Beyond just feeding and watering them, which is relatively straightforward, crocodiles also need to be captured for medical procedures, such as preventive vaccinations and health check-ups. This often requires catching several crocodiles at once.
Sasha and Pasha's father works with crocodiles, so the twins decided to build an automatic crocodile catcher as a gift for him. The device operates simply: it is placed near one wall of the crocodile terrarium, and a direction is chosen to shoot a long net with suction cups. The net adheres firmly to the opposite wall of the terrarium and is then tightly stretched, dividing the terrarium into two sections. Some crocodiles end up on the left side of the net, while others are on the right. The task is then to capture the crocodiles from the desired side.
To configure the device, Sasha and Pasha need a program that can determine which crocodiles are on the left and which are on the right for a given shooting direction. Your task is to write such a program.
The shooting direction, and thus the direction along which the net is stretched, is defined by two points (A = (x_a, y_a)) and (B = (x_b, y_b)). The normal to this vector is given by the vector ((-D_y, D_x)) where (D_y = y_b - y_a) and (D_x = x_b - x_a). Points located in the direction indicated by the normal are on the left, and all others are on the right. Naturally, there cannot be crocodiles in the direction in which the net is shot, as this would harm the crocodile and lead to the dismissal of Sasha and Pasha's father. The crocodiles are small, so each crocodile's position can be represented as a point.
Input
The input file starts with an integer (N) on the first line, representing the number of crocodiles in the terrarium ((0 < N 20)).
The following (N) lines contain the real coordinates of the points where the crocodiles are located.
The last line provides the description of the direction in which the crocodile catcher is shot, specified by four real numbers: the coordinates of two points (A = (x_a, y_a)), (B = (x_b, y_b)).
Output
For each shot, output the location of all crocodiles: the letter (L) at the (i)-th position indicates that the crocodile is on the left of the net, and the letter (R) indicates it is on the right.