CUBEFR  Cube Free Numbers
A cube free number is a number who’s none of the divisor is a cube number (A cube number is a cube of a integer like 8 (2 * 2 * 2) , 27 (3 * 3 * 3) ). So cube free numbers are 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18 etc (we will consider 1 as cube free). 8, 16, 24, 27, 32 etc are not cube free number. So the position of 1 among the cube free numbers is 1, position of 2 is 2, 3 is 3 and position of 10 is 9. Given a positive number you have to say if its a cube free number and if yes then tell its position among cube free numbers.
Input
First line of the test case will be the number of test case T (1 <= T <= 100000) . Then T lines follows. On each line you will find a integer number n (1 <= n <= 1000000).
Output
For each input line, print a line containing “Case I: ”, where I is the test case number. Then if it is not a cube free number then print “Not Cube Free”. Otherwise print its position among the cube free numbers.
Example
Sample Input: 10 1 2 3 4 5 6 7 8 9 10 Sample Output: Case 1: 1 Case 2: 2 Case 3: 3 Case 4: 4 Case 5: 5 Case 6: 6 Case 7: 7 Case 8: Not Cube Free Case 9: 8 Case 10: 9
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lotus_guy:
20141225 16:30:21
Simple BIT problem :) 

shubham:
20141223 11:54:29
sieves.....(y) 

Kid Algorist:
20141029 20:43:41
Great optimisations are possible in the problem.


Sumit Kumar Rakshit:
20141026 05:23:34
has nothing to do with the size of n, 1000000 woks fine.. @Sudipto :P 

Nishanth Vijayan:
20140921 00:01:05
@PurvaBaradia: look at your output carefully :) 

Never see me (saran):
20140828 15:05:02
nice question Last edit: 20140828 17:23:45 

PurvaBaradia:
20140826 13:48:54
can anyone tell me whats wrong with my code ? it gives wa for 0.45 sec http://ideone.com/gxoqvr 

****:
20140813 17:18:18
i used seive. can someone tell me what 's wrong in my code.. i got time limit exceeded.


« sudipto »:
20140722 07:16:27
take n<=1000100... it got me AC... n<=1000010 gets WA... : 

Suraj Rajan:
20140511 21:29:13
sieve works like a charm...!! :) 
Added by:  Muhammad Ridowan 
Date:  20110614 
Time limit:  0.100s1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own. For alternate thanks Sayef Azad Sakin 