CANTON - Count on Cantor

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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
Tony T.: 2015-04-01 05:04:12

Need to know a couple of equations on triangular numbers. The rest is just conceptualising how the terms move along the diagonal.

NESTOR IGNACIO BERNAL MORALES: 2015-03-05 22:29:57

Yeah

Yash: 2015-02-06 23:10:15

AC in 1st go :) My 75th on spoj :)

Pratik: 2015-01-29 06:58:45

How is third term not 1/3

Harsh Shah: 2015-01-28 19:17:53

Learnt new technique, great question.

:.Mohib.:: 2015-01-18 11:40:51

Easy...got It..... :)

SM_92: 2015-01-01 18:55:57

Last edit: 2015-01-03 09:35:52
Saksham : 2014-12-24 19:49:53

ac in first go
just focus diagnally

kartikay singh: 2014-12-11 07:13:32

AC in 0.0 sec yepieee

kartikay singh: 2014-12-11 07:12:41

silly mistakes cost me 2 WA but finally AC .........
dont forget to use long long int in c


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