Game Prediction

There are $M$ people, including you, playing a special card game. At the start, each player is dealt $N$ cards. Every card shows a distinct positive integer pip between $1$ and $N \times M$; no two cards share the same pip.

In each round, every player plays one of their cards and the cards are compared. The player who plays the card with the largest pip wins that round, and the next round begins. After $N$ rounds every card has been played, and the player who has won the most rounds wins the game.

Given the cards you were dealt, write a program that determines the maximum number of rounds you can guarantee to win, no matter how your opponents play.

The input consists of several test cases. The first line of each case contains two integers $m$ ($2 \le m \le 20$) and $n$ ($1 \le n \le 50$), the number of players and the number of cards each player is dealt. The next line contains $n$ positive integers, the pips of the cards you were dealt. A blank line separates consecutive cases.

The input is terminated by a line containing two zeros.

For each test case, print a line in the form Case x: y, where $x$ is the test case number (starting from $1$) and $y$ is the maximum number of rounds you can guarantee to win in that game.