Vasya and Tanks
Vasya, who is new to programming, has decided to enter a popular competition that involves programming the movement of a tank in a gaming environment. One challenge Vasya faces is understanding how tanks move. In this game, much like in reality, a tank can move forward or backward in a straight line, and it can also turn by creating an arc due to differences in track power. The greater the power difference, the sharper the turn. While watching other tanks, Vasya noticed that many of them turn in place before moving forward to change direction. He believes this wastes time and thinks it's better to move directly in the desired direction, even if it means traveling along an arc.
Your task is to help Vasya write a part of his program that determines the direction in which his tank should move: forward-left (denoted as forward left), forward-right (forward right), backward-left (backward left), or backward-right (backward right). It is guaranteed that the battlefield conditions ensure there is no ambiguity in choosing the direction. You can also assume the tank is infinitesimally small.
Input
The first line contains three real numbers: x_1, y_1, and angle. Here, x_1 and y_1 are the coordinates of the tank on the battlefield, and angle is the angle in degrees between the vector from the center of the tank along its longitudinal axis and the x-axis. The angle ranges from 0 to 360 degrees, with zero degrees indicating alignment with the x-axis, increasing counterclockwise. The second line contains two real numbers: x_2 and y_2, which are the coordinates of the point the tank should move towards. It is guaranteed that all coordinates and the angle angle are such that the direction can be determined without ambiguity.
Output
Output a single line indicating the direction of movement using the terms specified in the problem statement.