Kata

Mahjong Knowledge

Mahjong is based on draw-and-discard card games that were popular in 18th and 19th century China and some are still popular today.

In each deck, there are three different suits numbered 1 to 9, which are called Simple tiles. They are Circles (denoted by [1-9]p), Bamboo (denoted by [1-9]s), and Characters (denoted by [1-9]m).

Circles:
Bamboo:
Characters:

Moreover, there is another suit named Honor tiles. It includes Wind tiles (namely East, South, West, North, denoted by [1-4]z) and Dragon tiles (namely Red, Green, White, denoted by [5-7]z).

East Wind	South Wind	West Wind	North Wind

Red Dragon	Green Dragon	White Dragon

Note that there are EXACTLY 4 identical copies of each kind of tiles in a deck.

How to win the game of mahjong

A regular winning hand consists of 4 Melds and 1 Pair. Each meld of tiles can be 3 identical or consecutive tiles of a suit. For example:

3 identical tiles	3 consecutive tiles

Note that the Honor tiles ([1-7]z, winds and dragons) can ONLY be combined to a meld of 3 identical tiles.

A winning combination of mahjong pieces:

└────┴────┘ meld 1

└────┴────┘ meld 2

└────┴────┘ meld 3

└────┴────┘ meld 4

└───┘ pair 1

Task

Your task is to verify that a mahjong combination is correct. The mahjong combination is: JIU LIAN BAO DENG(九莲宝灯, Win for 9 pieces).

Rules

All mahjong pieces must from a same suits(Circles([1-9]p) or Bamboo ([1-9]s or Characters ([1-9]m)). The basic body is 13 pieces:"1x 1x 1x 2x 3x 4x 5x 6x 7x 8x 9x 9x 9x", x can replaced by p,s or m. And then add any one of the same suit will be able to win (because no matter what number to add, mahjong can be divided into 4 melds and 1 pair).

An example of JIU LIAN BAO DENG using circles:

1p 1p 1p 2p 3p 4p 5p 6p 7p 8p 9p 9p 9p + 9p
divided into 4 melds and 1 pair:
1p1p 1p2p3p 4p5p6p 7p8p9p 9p9p9p

Input

• A string denoting 14 tiles to be computed.

  "1p 1p 1p 2p 3p 4p 5p 6p 7p 8p 9p 9p 9p 9p"
  

  The order of the Mahjong pieces always be: p-->s-->m-->z and 1--->9

Output

• A boolean value. If the input string is a valid winning hand of "JIU LIAN BAO DENG", return true; If not, return false.

Series

• DA SI XI(大四喜)
• DA SAN YUAN(大三元)
• LV YI SE(绿一色)
• JIU LIAN BAO DENG(九莲宝灯)