CANTON - Count on Cantor

no tags 

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: 2014-10-26 17:12:39

u have to give more time to this,may use concept of triangular numbers

KAI: 2014-09-21 19:12:05

yeah 1st go :)

Siya: 2014-09-20 13:33:37

AC in first attempt :)

Nabeel: 2014-09-10 09:28:16

After a great thinking,,,, GOT AC :)

Abhishek Singh: 2014-08-20 19:25:13

help needed!
it is showing compilation error, but the code is compiled and running correctly on my computer! i m using C++ on Visual Studio 2013.

opcode: 2014-08-17 07:45:14

not able to completely understand the pattern, taken help from web :(

shreya sahu: 2014-08-10 22:29:35

green in first attempt! :)

sasuke: 2014-07-18 10:04:36

Got AC in the first attempt

Last edit: 2014-07-18 10:04:50
Shireen Nagdive: 2014-06-27 16:06:23

AC in one go :D :D

Steven Hans Limantoro: 2014-06-24 08:48:29

Just use Diagonal Argument :)

Last edit: 2014-06-24 08:48:46

Added by:Thanh-Vy Hua
Date:2005-02-27
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