#2484. Pku3915 Black Vienna

 This problem is based on the game of Black Vienna. In this version there are three players and 18 cards labeled A-R. Three of the cards are set aside (hidden) and form the "Black Vienna" gang. The remaining cards are shuffled and dealt to the players so that each player has 5 cards. Players never reveal their cards to each other. There is a separate deck of "interrogation cards" which contain three distinct letters in ascending order, like ACG or BHR. Turns rotate through players 1, 2, and 3. On each player's turn, that player selects an interrogation card, puts it face up in front of another player, and that other player must indicate the total number of these cards being held, without saying which ones. All players see the result of the "interrogation". The play continues until a player deduces the three cards in the "gang".
For example, suppose the cards are distributed as follows, and the game then proceeds:


Player 1: DGJLP; Player 2: EFOQR; Player 3: ACHMN; Gang: BIK

Turn 1: Player 1 interrogates player 2 with BJK; answer 0
Turn 2: Player 2 interrogates player 3 with ABK; answer 1
Turn 3: Player 3 interrogates player 2 with DEF; answer 2
Turn 4: Player 1 interrogates player 2 with EIL; answer 1
Turn 5: Player 2 interrogates player 3 with FIP; answer 0
Turn 6: Player 3 interrogates player 1 with GMO; answer 1
Turn 7: Player 1 interrogates player 2 with OQR; answer 3
Turn 8: Player 2 interrogates player 3 with ADQ; answer 1
Turn 9: Player 3 interrogates player 1 with EGJ; answer 2



In fact, the game does not need to get to turn 9. With enough thought, player 1 can deduce after turn 8 that the gang is BIK. It is your job to analyse records of games and deduce the earliest time that the gang could be determined for sure.


Black Vienna游戏是当前很流行的桌面游戏，规则是这样的：有18张牌，分别标着A-R，游戏有三个人。游戏开始的时候每个人拿5张牌，剩下三张牌隐藏起来，大家都只能看见自己手中的牌。之后，从第一个人到第三个人轮流拿一张“疑问牌”去问另外的一个人，“疑问牌”上有三个字母，那个人必须诚实地回答自己手中有多少疑问牌中的字母。哪个人能够最先推断出隐藏起来的牌是什么，那个人就取得胜利。现在你的任务是，给出三个人手上的牌和询问情况，你需要计算出最早在哪一次询问之后，有人能够推断出隐藏的牌。

样例输入

			
9

DGJLP EFOQR ACHMN BIK

2 BJK 0

3 ABK 1

2 DEF 2

2 EIL 1

3 FIP 0

1 GMO 1

2 OQR 3

3 ADQ 1

1 EGJ 2

3

ABCDE FGHIJ KLMNO PQR

3 BKQ 1

1 ADE 3

2 CHJ 2

0

样例输出

			
8

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