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 around 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 in one line.

Example

Input:
1 4
9 32
10 12
Output:
Case 1: 1
Case 2: 7
Case 3: impossible