Testing Ground
A renowned robotics company has developed a new model named Robotas-Barabas. This robot is operated through a wireless network channel using the visual programming environment RobotasBarabasView. Testing is conducted on a designated testing ground, which includes a large blue triangle. During these tests, the robot must remain within the boundaries of this triangle.
Given the coordinates of the triangle's vertices, determine which coordinate quadrants the robot can occupy and which it cannot.
For this task, the coordinate quadrants are defined as follows: the first quadrant – ({x>0, y>0}), the second quadrant – ({x<0, y>0}), the third quadrant – ({x<0, y<0}), and the fourth quadrant – ({x>0, y<0}).
Input
The input file consists of three lines, each containing two coordinates representing a vertex of the triangle. The coordinates are real numbers, each not exceeding (10^6), with up to two decimal places.
Output
For each quadrant, output on a separate line whether the robot can be located in it ("YES") or not ("NO").