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1220 - Mysterious Bacteria
  PDF (English) Statistics Forum
Time Limit: 0.5 second(s) Memory Limit: 32 MB

Dr. Mob has just discovered a Deathly Bacteria. He named it RC-01. RC-01 has a very strange reproduction system. RC-01 lives exactly x days. Now RC-01 produces exactly p new deadly Bacteria where x = bp (where b, p are integers). More generally, x is a perfect pth power. Given the lifetime x of a mother RC-01 you are to determine the maximum number of new RC-01 which can be produced by the mother RC-01.


Input starts with an integer T (≤ 50), denoting the number of test cases.

Each case starts with a line containing an integer x. You can assume that x will have magnitude at least 2 and be within the range of a 32 bit signed integer.


For each case, print the case number and the largest integer p such that x is a perfect pth power.

Sample Input

Output for Sample Input





Case 1: 1

Case 2: 30

Case 3: 2


Problem Setter: Muhammad Rifayat Samee
Special Thanks: Jane Alam Jan
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