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

hide comments
Subhendu Sethi: 2016-05-21 03:04:32

No need to Prime Factorize. Think about sieving! Easy.

mohitgupta07: 2016-05-13 22:36:02

dun knw why getting wrong answer -_- can anyone tell me dat how many cube free no.s lie in this range!!

ysn: 2016-05-02 15:04:45

@Sarthak Munshi 9 is a perfect square not a cube number. you are confusing addition with multiplication. 3+3+3=9 is not a cube number but 3*3*3=27 is a cube number.
Edit: it looks like you have already solved the problem. so my comment might be irrelevant to you.

can you please reply to my comment? its right under your question

Last edit: 2016-05-02 15:09:30
Sarthak Munshi: 2016-05-02 12:09:30

How can 18 be a cube free number ? 9 is a divisor of 18 and it is a cube .

ysn: 2016-04-12 13:38:29

@Muhammad Ridowan i wrote a code that doesnt even use a loop. but still i am getting TimeLimit exceeded. Why?

Setter ans: Java scanner is very slow. Use faster input methods

Last edit: 2016-06-03 13:20:46
ALi Ibrahim: 2016-04-10 22:26:35

My 50th on Spoj :D

pvsmpraveen: 2016-01-29 20:03:39

Cutest lowerbound ever

aakash_s: 2016-01-07 20:19:24

The same code in my compiler gave memory overflow ...when i realized there was none other option....i submitted and AC 0.03s

sy_117: 2015-10-23 20:41:23

Nice ques. learnt somthing new !!!!!

prakash_reddy: 2015-10-05 19:33:38

My 100th on Spoj.... prime factorization roxxxxxxxx.... :)


Added by:Muhammad Ridowan
Date:2011-06-14
Time limit:0.100s-1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own. For alternate thanks Sayef Azad Sakin