Degenerate Matrix

题目大意：给一个矩阵（如图），每个数可以加任意的数使得该矩阵为退化矩阵（ad-bc=0），求每个数加的数的绝对值最大的最小值。

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|<=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 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} $ .

1 2
3 4

0.2000000000

1 0
0 1

0.5000000000

In the first sample matrix $ B $ is  In the second sample matrix $ B $ is