DEA is currently struggling with a case of cooking Blue Crystal in Albuquerque. Hector Salamanca is a key witness of this case as he knows a lot of stuff regarding the Gang responsible for cooking & distribution of Blue Crystal.
"Hector Salamanca..? That Name rings a Bell!"
He agreed to tell everything he knows about this case to DEA. Gus Fring & Heisenberg are two people of the Gang which cook the Blue Crystal & they came to know about this. So, both of them want Hector to be dead before he tells anything to the DEA & Hank Schrader.
Heisenberg lives at a point (x1,y1) & Gus Fring at (x2,y2), both in Albuquerque.
Suddenly, DEA came to know that some of the Gang members want to kill Hector.
So, DEA is looking for a safe house along ax+by+c=0 (the border of Albuquerque), where they can ask Hector about the information he knew.
DEA also knows about the coordinates of Heisenberg & Gus & they want the safe house to be at a location which maximizes the difference between distance of the safe house to Heisenberg's House & distance of the safe house to Gus Fring's House.
Help DEA in finding the maximum absolute difference between the distance between safe house & Heisenberg’s house and distance between safe house & Gus Fring’s house i.e.
First line contains an integer T denoting the number of test case(s).
Each test case consists of two lines.
First line of each test case contains three integers a, b & c, describing the equation of the border of Albuquerque along which DEA is looking for a safe house.
Second line of each test case contains four integers x1, y1, x2, y2.
For each test case output the integral part of answer in separate line.
NOTE : Answer to the given problem always exists.
Equation of the line L (on which there is Safe House) is
Co-ordinates of the houses of Heisenberg & Gus are-
(x1,y1) ≡ (-1,4)
(x2,y2) ≡ (-8,-5)
Max. difference between the (Safe House - Heisenberg House length) & (Safe House - Gus Fring's House length) is approx. 11.401.
So the integral part (floor value) is 11.