PROGRAMMING:Three dimensional Pinball

You've all played 3D pinball. Now there is a simplified version of 3D pinball. At the beginning of the game, the pinball is in the middle of an equilateral triangle, and the pinball has an initial velocity. When the pinball hits the wall (that is, the edge of the triangle), the pinball will rebound (equivalent to the reflection of light on the mirror), and the speed remains unchanged after rebound. Unlike the original 3D pinball, the three walls move along the vertical direction of the wall at the same speed (think of the walls as planes that can penetrate each other). When the triangle shrinks to a point, the game ends. So the question is, when the game is over, how many meters has the ball rolled?
###Input format:
Multiple sets of data. In the first line of each group, enter four integers n, V1, V2, C (0 < = n, V1, V2 < = 100, - 180 < = C < = 180) to represent the side length of the triangle, the moving speed of the wall (M / s), the initial speed of the billiard ball (M / s), and the angle between the initial speed and the horizontal direction (degrees). Guarantee that V1 is not equal to 0.
###Output format:
At the end of the game, the distance of the billiard ball rolling (meters), retain 2 decimal places.
###Input example:
Here is a set of inputs. For example:
```in
1 1 1 45
```
###Output example:
The corresponding output is given here. For example:
```out
zero point two nine
```







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