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ZOJ Problem Set - 3921
Guan Dan

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Bob is playing a poker game called GuanDan. The rules are similar to PaoDeKuai and DouDiZhu. Basically, the game is played on two decks of poker with four jokers in total. And there are some specific patterns of hands that you can play. They will be listed below.

Notation
  • A card contains two characters
  • The first character is its rank, the second character is its suit
  • For an ordinary card, rank can be A, 2, 3, 4, 5, 6, 7, 8, 9, 0, J, Q, K (A for Ace, 0 for 10)
  • J, Q, K can be taken as 11, 12, 13 respectively. Ace can be taken as either 1 or 14.
  • Suit can be D, S, H, C (Diamond, Spade, Heart, Club)
  • So there are 13 * 4 = 52 different ordinary cards
  • Special cards: BJ, RJ (BJ for Black Joker, RJ for Red Joker)
  • So all cards are [A-K][DSHC]*2 + BJ*2 + RJ*2, in total 108 cards.
Hands you can play
Hand Description Example(s) Counter Example(s) Difficulty
Solo Any single card AS (Spade A) None 1
Pair Two cards of the same rank 0D 0C (Diamond 10 and Club 10) BJ RJ (Jokers of different colors doesn't count as the same rank) 1
Three Pairs Three pairs with continuous rank AH AS 2S 2H 3D 3C, QH QH KH KH AH AH KH KH AH AH 2H 2H 1
Trio Three cards of the same rank AH AH AS, 9H 9S 9C BJ BJ RJ 1
Full House A composite of a Trio and a Pair AH AH AS 2S 2H None 1
Airplane Two Trios with continuous rank AH AH AD 2H 2H 2D, KH KH KD AH AH AD None 1
Straight Five cards with continuous rank AH 2S 3H 4C 5H, 0C JD QH KH AS JD QH KH AS 2S 1
Straight Flush Five cards with continuous rank and the same suit AH 2H 3H 4H 5H, 0H JH QH KH AH QH KH AH 2H 3H 0
Bomb Four or more cards of the same rank 5H 5H 5S 5S, 8H 8H 8S 8S 8C 8C 8D 8D None 0
Clarification
  • Jokers' rank is not continuous with ordinary cards
  • RJs have the same rank, BJs have the same rank, but an RJ and a BJ do not have the same rank.
  • Ranks being continuous means they form a sequence of natural numbers such that each number is 1 plus the number before it
Special rules
  • There is a main rank for each game. It can only be one of A, 2, 3, ..., K.
  • The two cards of the main rank with a Heart suit are wildcards.
  • A wildcard can be used as any card except the jokers.
Goal

Your goal is to play your cards as fast as possible and win the game by first playing all of your cards. Therefore, Bob would like to know the least sum of difficulty value if he combine his cards into valid hands optimally.

Input

The first line is an integer of the number of test cases.

For each test case, the first line contains a character denoting the main rank (rank is in {'A', '2', '3', '4', '5', '6', '7', '8', '9', '0', 'J', 'Q', 'K'}). The second line contains 54 characters, two characters is a card. Format is the same as descripted in Notation section. Test cases are randomly "drawn" from random shuffled "decks".

Output

For each test case, output the minimum difficulty if you arrange the cards optimally into hands.

Sample Input

2
3
AD3D8H6HKCKS4DJC3H3C9H2C5H9SJD3CKH7CKCAH5H2C4C3SBJAC5S
6
KC0D4HKD6DJCKC2S8HADJD4D9C7SJH3SBJRJ2DQH5H8S9D5S0S2D5C

Sample Output

6
9

Hint

Here's one possible solution for sample 1 and sample 2.

Sample 1: 3H is a wildcard.

3H -> 3C
| AC AD AH 5H 5S || 3C 3D 3S JC JD || 9S || **KC KC KH KS** || BJ || 2C 2C 3C 3C 4C 4D || 5H 6H 7C 8H 9H |

KKKK is a bomb, it has difficulty 0. Others each have difficulty 1. Sum is 6.

Sample 2:

| 2D 2S || 4H || 5H 5S || JD JH KC KC KD || BJ || RJ || 8S 9D 0S JC QH || 6D 7S 8H 9C 0D || AD 2D 3S 4D 5C |

No bomb. Sum is 9.


Author: GONG, Yuan
Source: ZOJ Monthly, February 2016
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