A9510. Gena and Second Distance

Gena doesn't like geometry, so he asks you to solve this problem for him.

A rectangle with sides parallel to coordinate axes contains $n$ dots. Let's consider some point of the plane. Let's count the distances from this point to the given $n$ points. Let's sort these numbers in the non-decreasing order. We'll call the beauty of the point the second element of this array. If there are two mimimum elements in this array, the beaty will be equal to this minimum.

Find the maximum beauty of a point inside the given rectangle.

The first line contains three integers $w,h,n$ ( $1<=w,h<=10^{6},2<=n<=1000$ ) — the lengths of the rectangle sides and the number of points. Next $n$ lines contain two integers $x_{i},y_{i}$ ( $0<=x_{i}<=w,0<=y_{i}<=h$ ) each — the coordinates of a point. It is possible that it will be coincident points.

Print a single number — the maximum beauty of a point with the absolute or relative error of at most $10^{-9}$ .

The point which beauty we need to find must have coordinates ( $x,y$ ), where $0<=x<=w,0<=y<=h$ . Some of the $n$ points can coincide.