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Description

A projectile is fired into the air at an initial speed \(v_0\) and an initial angle \(\theta_0\), with an initial height \(h_0\). Its trajectory can be expressed as

\[y=h_0+\tan(\theta_0)x-\left(\frac{g}{2v_0^2\cos^2\theta_0}\right)x^2,\]

where \(g = 9.81\) is the gravitational acceleration constant.

Implement the bisection method to determine when the projectile touches the ground. Use the constant FLT_EPSILON as the convergence tolerance and \([75, 85]\) as the initial interval for the bisection method.

Hint 1: FLT_EPSILON is defined in <float.h> file and the mathematical functions are defined in <math.h>.
Hint 2: the trigonometric functions expect angles in radians.

Format

Files

You should submit a tar file containing a c source file ex4.c

Input

one line with a space separated list in the order \(v_0\) \(\theta_0\) height range_min range_max

Output

one line showing the result with six decimals

Sample 1

Input

30 30 1.5 75 85

Output

81.970131

Limitation

1s, 32MiB for each test case.