Codeforces Round #416 (Div. 2) has been moved to start on 27.05.2017 09:35 (UTC).
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

H. Degenerate Matrix

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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*||.

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

In the second sample matrix *B* is

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/26/2017 19:48:40 (c4).

Desktop version, switch to mobile version.
User lists

Name |
---|