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Problem 2264 Card Game (First Edition)

Accept: 317    Submit: 812
Time Limit: 1000 mSec    Memory Limit : 32768 KB

Problem Description

Fat brother and Maze are playing a kind of special (hentai) game with some cards. There are N*2 cards in this game for the players to use, this is the card deck. The game goes for N rounds and in each round, Fat Brother would draw one card from the remaining card deck randomly and then Maze would draw one card from the remaining card deck randomly. Then they compare for the integers which is written on these two cards. The player with the higher number wins this round and score 1 victory point. And then these two cards are removed from the game such that they would not appear in the later rounds. As we all know, Fat Brother is very clever, so he would like to know the expect number of the victory points he could get if he knows all the integers written in these cards.

Note that the integers written on these N*2 cards are pair wise distinct. At the beginning of this game, each player has 0 victory point.


The first line of the data is an integer T (1 <= T <= 100), which is the number of the text cases.

Then T cases follow, each case contains an integer N (1 <= N<=10000) which described before. Then follow one line with N*2 integers, which indicate the integers in these cards.

All the integers are positive and no morethan 10000000.


For each case, output the case number first, and then output the expect number of the victory points Fat Brother could get in this game. The answer should be rounded to 2 digits after the decimal point.

Sample Input

2 1 1 2 2 1 2 3 4

Sample Output

Case 1: 0.50 Case 2: 1.00



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