PHT  Pigeonhole Tower
Pigeon SSNA want to build a tower with some wood walls. Let's describe the tower they want to make:
 A Tower can consist of different number of level.
 If a tower contain L levels then 1^{st} level must contain L holes , 2^{nd} level L1 , 3^{rd} level L2 ….. L level contain 1 hole .
 Each room contain 3 wood walls.
See the picture below:
3 Level Tower  4 Level tower 
Now pigeon SSNA has n wood walls. What is maximum number of level he can made.
Input
Input starts with an integer T (≤ 100000), denoting the number of test cases.
Each case starts with a line containing an integer n (1 ≤ n ≤ 10^{12})
Output
For each case of input you have to print the case number and expected answer.
Sample Input 
Output for Sample Input 
2 15 24 
Case 1: 3 Case 2: 4 
hide comments
sagar_zhcet:
20170613 21:33:55
please someone explain the sample input and output Last edit: 20170613 21:34:07 

ankit1cool:
20170603 18:40:03
Watch for the "Case" it has capital "C" that caused me 2 WA 

vivek_prime:
20170603 10:25:03
what do holes mean here i m not getting this point. 

ayushgupta1997:
20170602 07:57:32
easy one :) quadratic ac in one go!!! ,loop costed one tle :( 

banneq:
20170418 12:30:08
Wrong output format costed me 5 WA, take care of "Case i: result"! 

Saif :
20160818 10:51:44
ac in 1 go!! use recurrence relation! 

sharif ullah:
20160804 21:29:49
9th class series summation formula + binary search!!! accepted Last edit: 20160804 21:31:00 

raghav12345:
20151114 10:56:25
easy one apply simple math formula 

Manish Das Mohapatra:
20150821 21:16:01
There's space between Colon and Result in the Output format.


Ravi Chandra:
20150821 20:51:08
Easy prob....TLE Once..Loop modified...AC 
Added by:  Ajharul Islam Barid 
Date:  20141013 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU 
Resource:  Own Problem 