Description

Given a straight line and two points P, Q on the plane, you should find a point V on the line, such that |PV|+|QV| is minimal.

 

Input

The first line is number of test cases.

For each test case, there are two lines:

Line 1: 4 real numbers – coordinates of P and Q;

Line 2: 3 real numbers, a, b, and c – coefficients of a straight line ax + by + c = 0(a2+b20).

 

Output

For each test case, output one line containing one real number – the minimal distance. Be accurate to 1 digit after decimal point.

 

Sample Input

2

0 2 1 3

1 1 -2

2 2 6 1

0 1 0

 

Sample Output

1.4

5.0