Yay! Small Small Blue finally managed to buy a tiny plot of land just about 10 kilometers from Shanghai Bund. Only... only it was so expensive that he is no more able to afford building a house there. So he decide to go for a swimming pool. It should have the form of circle, and be as big as possible inside his plot. Having carefully measured the border of his plot, he know now that it is a convex N-gon.
What is the largest possible radius of a circular pool in it?
There are multiple test cases in the input. There are at most 25 groups.
The first line of each case contains an integer N, 3≤N≤15000. The next N lines contain two integers each, xi and yi, not exceeding 107 by absolute value — the coordinates of the vertices of the plot (a convex polygon) in the counter-clockwise direction. No three vertices lie on the same line.
For each test case, output the sought radius. Absolute or relative difference between real answer and your solution should be less than 10-6.