The largest circle
Congratulations! You've finally acquired a piece of land nearly 400 kilometers from Kyiv. However, it was so costly that building a house is out of reach for now. Instead, you've decided to construct a swimming pool. The pool should be circular and as large as possible within the boundaries of your plot. After carefully measuring the plot, you know it forms a convex N-gon.
What is the maximum possible radius of the circular pool that can fit inside this plot?
Input
The first line of the input contains an integer N, where 3 ≤ N ≤ 10000. The following N lines each contain two integers, x_i and y_i, with absolute values not exceeding 10^7. These represent the coordinates of the vertices of the plot (convex polygon) listed in counterclockwise order. No three vertices are collinear.
Output
Output the maximum possible radius of the circular pool. The result should be accurate to 3 decimal places.