Problem Description

A cup is placed in an opaque box. The base of the cup can be regarded as a circle. The box can be regarded as a rectangular cuboid, and its thickness can be ignored.

Now place the bottom face of the box in a 2D Cartesian coordinate system. Its four vertices are at $(0,0)$, $(x,0)$, $(0,y)$, and $(x,y)$.

You only know that the center of the circular base of the cup is at $(p,q)$. What is the maximum possible radius of the cup’s base?

Input Format

Only one line is given, containing four integers $x,y,p,q$.

Output Format

Output only one number: the maximum possible radius of the cup’s base.

10 5 3 4

1

Hint

Explanation for Sample #1

The situation where the cup radius is the largest is shown in the figure below.

Constraints

For $100\%$ of the testdata, $0<p<x\le100$ and $0<q<y\le100$.

Special Property A: $x=y$.

Special Property B: $x=2p,y=2q$. That is, the center of the cup’s base is at the geometric center of the box’s bottom face.

Translated by ChatGPT 5