Cole is a programmer in the coal division of Metal (previously Facebulk), working across (T) office buildings with very pleasant coworkers and unlimited free ice cream. However, as a self-proclaimed antisocial code monkey, he still prefers to "mine" his own business when possible.

A given office building can be represented by an axis-aligned rectangle with opposite corners ((0, 0)) and ((X_R, Y_R)) on a 2D plane. Inside, there are (N) friendly coworkers, the (i)th of whom is permanently seated at position ((X_i, Y_i)), distinct from all other coworkers.

Cole is currently at position ((X_A, Y_A)), and would like to reach the unlimited free ice cream at a different position ((X_B, Y_B)). Neither position is located at a coworker's seat.

Please help Cole determine the closest distance he'll need to get to another coworker in order to travel from ((X_A, Y_A)) to ((X_B, Y_B)) without leaving the building. Your answer will be accepted if it is within either (10^{-6}) or (0.000001%) of the right answer.

Constraints

(1 \le T \le 800) (1 \le N \le 800{,}000) (2 \le X_R, Y_R \le 1{,}000{,}000{,}000) (0 < X_i, X_A, X_B < X_R) (0 < Y_i, Y_A, Y_B < Y_R)

The sum of (N) across all buildings is at most (3{,}000{,}000).

Input

Input begins with a single integer (T), the number of office buildings. For each building, there is first a line containing (2) space-separated integers, (X_R) and (Y_R). Then, there is a line containing (4) space-separated integers, (X_A), (Y_A), (X_B), and (Y_B). Then, there a line containing a single integer (N). Then, (N) lines follow, the (i)th of which consists of (2) space-separated integers, (X_i) and (Y_i).

Output

For the (i)th building, print a line containing "Case #i: " followed by a single real number, the closest that Cole will need to get to another coworker in order to reach the free ice cream.

Sample Explanation

In the first building, walking directly from ((3, 1)) to ((17, 1)) would take Cole within just 2 units of the coworker at ((10, 3)). Instead, one optimal route might involve walking upward first, then across, and then back down, as illustrated below:

The closest such a route gets to the coworker is (7) units (for example at coordinates ((10, 10)).

In the second building, Cole's route must begin and end at a distance of (\sqrt{4^2 + 2^2} \approx 4.47) units from the coworker at ((10, 3)). It's possible for Cole to get around them without getting any closer than that, for example with the following route:

In the third building, one optimal route for Cole might look as follows: