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

H. Degenerate Matrix
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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||.

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.

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