#P549H. Degenerate Matrix
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ID: 3275
Type: Default
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Degenerate Matrix
No submission language available for this problem.
Description
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| ≤ 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 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.
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.
Samples
1 2
3 4
0.2000000000
1 0
0 1
0.5000000000
Note
In the first sample matrix B is
In the second sample matrix B is