Degenerate Matrix

1000ms

262144K

Description:

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

$\text{[math]}$

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 $\text{[math]}$ . 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| ≤ 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:

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.

Sample Input:

1 2
3 4

Sample Output:

0.2000000000

Sample Input:

1 0
0 1

Sample Output:

0.5000000000

Note:

In the first sample matrix B is $\text{[math]}$

In the second sample matrix B is $\text{[math]}$

Informação

Provedor Codeforces

Código CF549H