BREAKING - Number Breaking


Every number is multiplication of some prime numbers. Prime number is a number which is only divided by 1 and itself. Here you are given a number n. You have to find the prime numbers whose multiplication makes this number.

For example, 12 is multiplication of prime numbers 2 and 3. 15 is multiplication of 3 and 5.

Input

First Line will contain the number of test cases T. Then each line will contain a single integer n.

Constraints: 1≤T≤1000, 2≤n≤1000000.

Output

For each test case print a single line which contains test case number and the prime numbers in ascending order separated by a single space whose multiplication make this number.

Example

Input:
3
12
42
84 Output: Case 1: 2 3
Case 2: 2 3 7
Case 3: 2 3 7
 

hide comments
Reayz: 2017-03-09 19:22:46

good one...

Md Jahidul Hasan: 2017-03-09 05:21:49

A Very Good Basic Problem.

Last edit: 2017-03-09 05:22:10

Added by:Shakil
Date:2017-03-09
Time limit:1s-2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All