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Задачі

A Famous Grid

A Famous Grid

Ліміт часу 3 секунди
Ліміт використання пам'яті 32 MiB

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.

Вхідні дані

Each test case is described by a line of input containing two nonprime integer 1x, y10000.

Вихідні дані

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

Приклад

Вхідні дані #1
1 4
9 32
10 12
Вихідні дані #1
Case 1: 1
Case 2: 7
Case 3: impossible
Джерело ACM ICPC Fudan Local Programming Contest 2012