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Problem 1149 Conic distance

Accept: 99    Submit: 194
Time Limit: 1000 mSec    Memory Limit : 32768 KB

Problem Description

A cone is located in 3D such that its base of radius r is in the z = 0 plane with the center at (0,0,0). The tip of the cone is located at (0, 0, h). Two points are given on the cone surface in conic coordinates. The conic coordinates of a point p lying on the surface of the cone are two numbers: the first, d, is the distance from the tip of the cone to p and the second, A < 360, is the angle in degrees between the plane y = 0 and the plane through points (0,0,0), (0,0,h) and p, measured counterclockwise from the direction of the x axis.


Input

Given are two points p1 = (d1, A1) and p2 = (d2, A2) in the conic coordinates.

Output

What is the (shortest) distance between p1 and p2 measured on the surface of the cone?

Sample Input

3.0 4.0 2.0 0.0 4.0 0.0 3.0 4.0 2.0 90.0 4.0 0.0 6.0 8.0 2.14 75.2 9.58 114.3 3.0 4.0 5.0 0.0 5.0 90.0

Sample Output

2.00 3.26 7.66 4.54

Source

Albert 2001

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