CF2254A Riptide

Alice, Bob, and Charlie are playing a game with tokens. They start with $ a $ , $ b $ , and $ c $ tokens, respectively. The game is played in rounds. Before the beginning of each round, they check the number of tokens everyone has: - If any two players have the exact same number of tokens, the game immediately ends. - Otherwise, the round begins, all three players have a strictly different number of tokens. The player with the strictly most tokens gives exactly $ 1 $ token to the player with the strictly fewest tokens. Given the starting tokens $ a $ , $ b $ , and $ c $ , determine exactly how many rounds the game will last before it ends.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^3 $ ) — the number of test cases. Each test case consists of a single line containing three integers $ a $ , $ b $ , and $ c $ ( $ 1 \le a, b, c \le 10 $ ).

For each test case, output a single integer — the number of rounds the game will last before it ends.

In the first test case: - No two players have the same number of tokens. - Charlie has the most tokens ( $ 3 $ tokens), and Alice has the fewest tokens ( $ 1 $ token). Therefore, Charlie gives Alice a token. - Now, Alice has $ 2 $ tokens, Bob has $ 2 $ tokens, and Charlie has $ 2 $ tokens. Since there are two players (or more) with the same number of tokens, the game ends. The game ended after $ 1 $ round, so the answer is $ 1 $ . In the second test case, the game is played as follows: - Bob gives Charlie a token, now Alice has $ 4 $ tokens, Bob has $ 5 $ tokens, and Charlie has $ 2 $ tokens. - Bob gives Charlie a token, now Alice has $ 4 $ tokens, Bob has $ 4 $ tokens, and Charlie has $ 3 $ tokens. Since two players have the same number of tokens, the game ends. The game lasted $ 2 $ rounds. In the third test case, two players already have the same number of tokens. So the answer is $ 0 $ since no rounds were played.