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A Famous Grid

Time Limit: 10000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2443    Accepted Submission(s): 918


Problem Description
Mr. B has recently discovered the grid named "spiral grid".
Construct the grid like the following figure. (The grid is actually infinite. The figure is only a small part of it.)


Considering traveling in it, you are free to any cell containing a composite number or 1, but traveling to any cell containing a prime number is disallowed. You can travel up, down, left or right, but not diagonally. Write a program to find the length of the shortest path between pairs of nonprime numbers, or report it's impossible.

 

Input
Each test case is described by a line of input containing two nonprime integer 1 <=x, y<=10,000.
 

Output
For each test case, display its case number followed by the length of the shortest path or "impossible" (without quotes) in one line.
 

Sample Input
1 4 9 32 10 12
 

Sample Output
Case 1: 1 Case 2: 7 Case 3: impossible
 

Source
 

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