In an episode of the Dick Van Dyke show, little Richie
connects the freckles on his Dad’s back to form a picture of
the Liberty Bell. Alas, one of the freckles turns out to be a
scar, so his Ripley’s engagement falls through.
Consider Dick’s back to be a plane with freckles at various
$(x, y)$ locations. Your
job is to tell Richie how to connect the dots so as to minimize
the amount of ink used. Richie connects the dots by drawing
straight lines between pairs, possibly lifting the pen between
lines. When Richie is done there must be a sequence of
connected lines from any freckle to any other freckle.
The input begins with a single positive integer on a line by
itself indicating the number of the cases (at most 20)
following, each of them as described below. This line is
followed by a blank line, and there is also a blank line
between two consecutive inputs.
The first line of test case contains $0 < n \le 1000$, the number of
freckles on Dick’s back. For each freckle, a line follows; each
following line contains two real numbers indicating the
$(x,y)$ coordinates of the
freckle. The coordinates will be at most $100\, 000$ in absolute value.
For each test case, your program should print a single real
number to two decimal places: the minimum total length of ink
lines that can connect all the freckles. Put a blank line
between outputs for consecutive test cases.
|Sample Input 1
||Sample Output 1