You are given a football field in 3D space. A ball is initially placed at point $$$(x, y, z)$$$. In front of the ball, there is a goal — a rectangular box from point $$$(0, 0, 0)$$$ to $$$(A, B, C)$$$.

After a kick, the ball starts flying with initial speed $$$v$$$ in a direction defined by two angles:

• $$$\theta$$$ — horizontal angle in degrees,
• $$$\phi$$$ — vertical angle in degrees.

At each moment of time $$$t \ge 0$$$, the position of the ball is given by:

$$$X(t) = x + v \cdot \cos(\phi) \cdot \cos(\theta) \cdot t$$$

$$$Y(t) = y + v \cdot \cos(\phi) \cdot \sin(\theta) \cdot t$$$

$$$Z(t) = z + v \cdot \sin(\phi) \cdot t - \frac{1}{2} \cdot g \cdot t^2$$$

where $$$g = 9.81$$$ and angles are converted to radians:

$$$\theta_\text{rad} = \theta \cdot \pi / 180$$$, $$$\phi_\text{rad} = \phi \cdot \pi / 180$$$.

You need to determine whether the ball will ever enter the goal volume.

The ball is considered inside the goal if at some moment $$$t \ge 0$$$ its position $$$(X(t), Y(t), Z(t))$$$ satisfies all of the following:

$$$0 \le X(t) \le A$$$, $$$0 \le Y(t) \le B$$$, $$$0 \le Z(t) \le C$$$