You have been given the job of forming the quiz teams for the next ‘MCA CPCI Quiz Championship’. There are 2 ∗ N students interested to participate and you have to form N teams, each team consisting of two members. Since the members have to practice together, all the students want their members house as near as possible. Let x1 be the distance between the houses of group1, x2 be the distance between the houses of group2 and so on.

You have to make sure the summation (x1 +x2 +x3 + . . .+xn ) is minimized.

Input

There will be many cases in the input file. Each case starts with an integer N (N ≤ 8).

The next 2 ∗ N lines will given the information of the students. Each line starts with the students name, followed by the x coordinate and then the y coordinate. Both x, y are integers in the range 0 to 1000. Students name will consist of lowercase letters only and the length will be at most 20.

Input is terminated by a case where N is equal to 0.

Output

For each case, output the case number followed by the summation of the distances, rounded to 2 decimal places. Follow the sample for exact format.