Inexactness of projectile hit may be compensated
by increasing of the projectile diameter.
In the problem you are to determine the minimal diameter that may compensate
inexactness of projectile hit in each concrete case. Assume that all the
targets are convex polygons. A hit is the situation when the circle crater
that the projectile leaves (the crater diameter equals to the one of the
projectile) covers at least one point of the target.
The first line contains three numbers — coordinates of the hit point of the projectile center and the number of polygon sides N (3 ≤ N ≤ 100). The next N lines contain the vertices coordinates in counter-clockwise order. All the coordinates are integers from [−2000,2000].
You are to output the only number which is the minimal diameter of a projectile that will cover the target rounded with three digits after the decimal point.
2 -1 8
Problem Author: Anton Botov and Anatoly Uglov
Problem Source: USU Open Collegiate Programming Contest October'2002 Junior Session