Description:
The determinant of a matrix 2 × 2 is defined as follows:
$$\operatorname*{det}\left(\begin{array}{cc}
a & b \\
c & d
\end{array}\right) = ad - bc$$
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 $${\boldsymbol{A}}={\begin{pmatrix}a&b\\c&d\end{pmatrix}}$$. Consider any degenerate matrix B such that norm ||A - B|| is minimum possible. Determine ||A - B||.
Input Format:
The first line contains two integers a and b (|a|, |b| ≤ 109), the elements of the first row of matrix A.
The second line contains two integers c and d (|c|, |d| ≤ 109) the elements of the second row of matrix A.
Output Format:
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.
Note:
In the first sample matrix B is $${ \left( \begin{array} { l l } { 1. 2 } & { 1. 8 } \\ { 2. 8 } & { 4. 2 } \end{array} \right) }$$
In the second sample matrix B is $${ \left( \begin{array} { l l } { 0. 5 } & { 0. 5 } \\ { 0. 5 } & { 0. 5 } \end{array} \right) }$$