TPS

TPS (third-person shooter) is a game played from a third-person camera that watches the protagonist, not from the protagonist's own first-person view. Because the player moves a free camera, the game can be enjoyed from many angles. This problem simulates such a TPS game and finds how the positions of the protagonist and the camera change with each input.

Protagonist and camera

The protagonist and the camera are on a 2D coordinate plane, and their positions are integer coordinates $(x,y)$. At the start, the protagonist is at $(0,0)$. The camera is always on the circle of radius $1$ centered at the protagonist, and it starts at $(0,-1)$. The camera always faces the protagonist.

Each time the player presses a key or moves the mouse, the protagonist, the camera, or both change position as follows. After each move, the protagonist and the camera are still at integer coordinates.

• Pressing W moves both the protagonist and the camera forward by $1$, where forward is the direction the camera faces.
• Pressing A moves both the protagonist and the camera left by $1$, taking the camera's facing direction as forward.
• Pressing S moves both the protagonist and the camera backward by $1$, taking the camera's facing direction as forward.
• Pressing D moves both the protagonist and the camera right by $1$, taking the camera's facing direction as forward.
• Moving the mouse to the right rotates the camera $90^{\circ}$ clockwise around the protagonist on the circle of radius $1$.
• Moving the mouse to the left rotates the camera $90^{\circ}$ counterclockwise around the protagonist on the circle of radius $1$.

The first line contains an integer $N(1\le N\le 100)$. From the second line onward, the $N$ player inputs are given in the order they were entered. Each input is one of W, A, S, D, MR, or ML. W, A, S, and D mean the corresponding keyboard key was pressed, MR means the mouse was moved to the right, and ML means the mouse was moved to the left.

On each of $N$ lines, print the protagonist's coordinates $(x\_p,y\_p)$ and the camera's coordinates $(x\_c,y\_c)$ after the $i$-th input ($1\le i\le N$), as $x\_p,y\_p,x\_c,y\_c$ separated by spaces.