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Another Eight Puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1294    Accepted Submission(s): 814


Problem Description
Fill the following 8 circles with digits 1~8,with each number exactly once . Conntcted circles cannot be filled with two consecutive numbers.
There are 17 pairs of connected cicles:
A-B , A-C, A-D
B-C, B-E, B-F
C-D, C-E, C-F, C-G
D-F, D-G
E-F, E-H
F-G, F-H
G-H

Filling G with 1 and D with 2 (or G with 2 and D with 1) is illegal since G and D are connected and 1 and 2 are consecutive .However ,filling A with 8 and B with 1 is legal since 8 and 1 are not consecutive .

In this problems,some circles are already filled,your tast is to fill the remaining circles to obtain a solution (if possivle).
 

Input
The first line contains a single integer T(1¡ÜT¡Ü10),the number of test cases. Each test case is a single line containing 8 integers 0~8,the numbers in circle A~H.0 indicates an empty circle.

 

Output
For each test case ,print the case number and the solution in the same format as the input . if there is no solution ,print ¡°No answer¡±.If there more than one solution,print ¡°Not unique¡±.
 

Sample Input
3 7 3 1 4 5 8 0 0 7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
 

Sample Output
Case 1: 7 3 1 4 5 8 6 2 Case 2: Not unique Case 3: No answer
 

Source
 

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