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Competitions

Marathon weekend with restrictions

Area Ratio

To make things easier, WishingBone decides to put this simple geometry problem at the beginning. Given a triangle, what is the ratio of the area of its inscribed circle to that of its circum circle?

prb1115

Input

9 integers x1, y1, z1, x2, y2, z2, x3, y3, z3 (-1000xi, yi, zi1000) are given on each line, the coordinates of triangle vertices. No three points are collinear.

Output

For each test case print the ratio on a separate line with three decimal digits. If rounding to a given accuracy you get zero, print the message "Zero!" (without the quotes).

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
0 0 0 0 0 1 0 1 0
Output example #1
0.172
Source Stage II All-Ukrainian Olympiad 2010-2011 Berdichev