Cover the Holes

A rectangular steel plate contains $N$ circular holes with a diameter of 5 mm, located at distinct, non-overlapping points - that is, the center of each hole is at a distance greater than or equal to 5 mm from the center of all other holes.

A circular piece, with a 5 mm diameter axis at its center, must be placed on the plate so that the axis fits into one of the plate's holes.

You need to write a program to determine the minimum diameter that the circular piece must have so that, with its axis fitted into one of the plate's holes, it completely covers all the other holes on the plate.

Input

The input consists of several test sets. The first line of a test set contains an integer $N$, which indicates the number of holes in the steel plate. The following $N$ lines each contain two integers $X$ and $Y$, separated by a blank space, describing the position of the center of a hole. The unit of measure of the holes' coordinates is 1 mm. The end of the input is indicated by $N = 0$.

Output

For each test set from the input, your program should produce three lines in the output. The first line should contain an identifier of the test set, in the format "Test n", where $n$ is numbered sequentially from 1. The second line should contain the minimum diameter that the circular piece must have, as an integer. The third line should be left blank. The spelling shown in the Output Example, below, must be followed rigorously.

Constraints

• $0 \leq N \leq 1000$ ($N = 0$ only indicates the end of the input)
• $-10000 \leq X \leq 10000$
• $-10000 \leq Y \leq 10000$