The determinant of a matrix 2 × 2 is defined as follows:$\operatorname{det} \left(\begin{array}{ll}{a} & {b} \{c} & {d} \end{array} \right) = a d - b c$

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 $A = \left(\begin{array}{ll}{a} & {b} \{c} & {d} \end{array} \right)$. Consider any degenerate matrix B such that norm ||A - B|| is minimum possible. Determine ||A - B||.

-----Input-----

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-----

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}.

-----Examples-----

Input 1 2 3 4

Output 0.2000000000

Input 1 0 0 1

Output 0.5000000000

-----Note-----

In the first sample matrix B is $\left(\begin{array}{ll}{1.2} & {1.8} \{2.8} & {4.2} \end{array} \right)$

In the second sample matrix B is $\left(\begin{array}{ll}{0.5} & {0.5} \{0.5} & {0.5} \end{array} \right)$