A9920 | Degenerate Matrix

The determinant of a matrix $2×2$ is defined as follows:

A matrix is called degenerate if its determinant is equal to zero.

The norm $||A||$ of a matrix $A$ is defined as a maximum of absolute values of its elements.

You are given a matrix . Consider any degenerate matrix $B$ such that norm $||A-B||$ is minimum possible. Determine $||A-B||$ .

The first line contains two integers $a$ and $b$ ( $|a|,|b|<=10^{9}$ ), the elements of the first row of matrix $A$ .

The second line contains two integers $c$ and $d$ ( $|c|,|d|<=10^{9}$ ) the elements of the second row of matrix $A$ .

Output a single real number, the minimum possible value of $||A-B||$ . Your answer is considered to be correct if its absolute or relative error does not exceed $10^{-9}$ .