Yay! You've finally managed to buy a tiny plot of land just about 400 kilometers from Moscow. Only... only it was so expensive that you are no more able to afford building a house there. So you decide to go for a swimming pool. It should have the form of circle, and be as big as possible inside your plot. Having carefully measured the border of your plot, you know now that it is a convex n-gon.

What is the largest possible radius of a circular pool in it?

Input

The first line contains an integer n (3 ≤ n ≤ 10000). 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.

Output

Output the sought radius with 3 digits after the decimal point.