CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
mohmmad ali:
20141026 17:12:39
u have to give more time to this,may use concept of triangular numbers 

KAI:
20140921 19:12:05
yeah 1st go :) 

Siya:
20140920 13:33:37
AC in first attempt :) 

Nabeel:
20140910 09:28:16
After a great thinking,,,, GOT AC :)


Abhishek Singh:
20140820 19:25:13
help needed!


opcode:
20140817 07:45:14
not able to completely understand the pattern, taken help from web :( 

shreya sahu:
20140810 22:29:35
green in first attempt! :) 

sasuke:
20140718 10:04:36
Got AC in the first attempt Last edit: 20140718 10:04:50 

Shireen Nagdive:
20140627 16:06:23
AC in one go :D :D 

Steven Hans Limantoro:
20140624 08:48:29
Just use Diagonal Argument :) Last edit: 20140624 08:48:46 
Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM South Eastern European Region 2004 