Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

Problem D

Constrained Exchange Sort

Input : standard input

Output : standard output

Given a permutation of 12 letters 'A'-'L', you are invited to write a program to sort them in ascending order under the following set of constraints:

q       The only allowed operation is the exchange of letters between two locations (locations are numbered from 1 to 12).

q       The letter 'L' must be involved in each operation.

q       The letter 'L' at location l₁ can be swapped with the letter at location l₂ provided l₁ ~ l₂ = d_i and floor((l₁ - 1) / d_{i + 1}) = floor((l₂ - 1) / d_{i + 1})for i = 1 | 2 | 3, where (d₁, d₂, d₃, d₄) = (1, 3, 6, 12).

q       You must use the minimum number of exchange operations possible.

Input

The first line of the input file contains an integer representing the number of test cases to follow.

Each test case contains a permutation of the letters 'A'-'L' on a line by itself. It is guaranteed that the given permutation can be sorted in ascending order under the given set of constraints.

Output

For each test case first output the permutation number on a line by itself. The next line will contain a sequence of letters where the letter at location i represents the letter with which 'L' is swapped in the i-th exchange during the sorting process. Output an empty line after each test case.

Sample Input

Sample Output