#Lutece0135. Mahjong

Mahjong

Migrated from Lutece 135 Mahjong

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Description

Mahjong is a wonderful game which origins from China (or maybe Korea because everything is Korean).

Mahjong is also a complex game. But the game we play here is rather easy. It just contains three suits: stones, bamboos and characters.

Stones consist of a number of circles. Each circle is said to represent can (筒, tóng) coins with a square hole in the middle.

Bamboos consist of a number of bamboo sticks. Each stick is said to represent a string (索, suǒ) that holds a hundred coins. Note that 11 Bamboo is an exception: it has a bird sitting on a bamboo, to prevent alteration.

Each character represents ten thousand (萬, wàn) coins.

A player wins the round by creating a standard mahjong hand, which consists of a certain number of melds (namely, four for 1313-tile variations) and a pair. A meld is three tiles which are adjacent in one suit or all the same. A pair is two same tiles.

Now one player has three tiles in hand. Can you tell what more tile he need to win?

Note that the number of each tile in Mahjong is four. So if the number of one tile the player has is four, he cannot get this tile anymore.

Input

The first line contains one integer TT indicating the number of test cases.

For each case, there are thirteen tiles in one line, separated by one space.

Each tile has two characters. The first character is 1 to 9 and the second is s (for stone), b (for bamboo), or c (for character).

Output

For each case, output one line containing the case number and all the tiles he needs to win the round, separated by one space.

If he needs more than one tile, first output stone, then bamboo, finally character, all from 11 to 99.

If he cannot win after get any tile, output None instead.

Please follow the format of the sample output.

Samples

5 
1b 1b 2b 2b 3b 3b 5s 6s 7s 1c 1c 2c 2c 
3s 4s 4s 5s 5s 5s 6s 6s 7s 9c 9c 4c 5c 
1s 1s 1s 2s 3s 4s 5s 6s 7s 8s 9s 9s 9s 
4b 5b 6b 7b 8b 8b 8b 2b 3b 4b 5s 6s 7s 
4c 5c 6c 9b 9b 9b 9b 1s 2s 3s 2s 3s 4s
Case 1: 1c 2c
Case 2: 3c 6c
Case 3: 1s 2s 3s 4s 5s 6s 7s 8s 9s
Case 4: 1b 3b 4b 6b 7b 9b
Case 5: None

Note

In case 33, if the player gets 1s, he can combine them into four melds 1s1s1s, 1s2s3s, 4s5s6s, 7s8s9s and a pair 9s9s. And so it is with 2s to 9s.

2s: 1s1s1s, 3s4s5s, 6s7s8s, 9s9s9s, 2s2s 
3s: 1s2s3s, 3s4s5s, 6s7s8s, 9s9s9s, 1s1s 
4s: 1s1s1s, 2s3s4s, 4s5s6s, 7s8s9s, 9s9s 
5s: 1s1s1s, 2s3s4s, 6s7s8s, 9s9s9s, 5s5s 
6s: 1s2s3s, 4s5s6s, 6s7s8s, 9s9s9s, 1s1s 
7s: 1s1s1s, 2s3s4s, 5s6s7s, 7s8s9s, 9s9s 
8s: 1s1s1s, 2s3s4s, 5s6s7s, 9s9s9s, 8s8s 
9s: 1s2s3s, 4s5s6s, 7s8s9s, 9s9s9s, 1s1s

Resources

The 5th Guangting Cup Central China Invitatio