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
dileep_32: 2021-03-19 04:01:11

GIVEN TEST CASE IS CORRECT

tejasreddyk: 2021-01-16 17:25:49

HHAHA AC in one go

naveen1948: 2020-11-08 08:19:10

check the output format carefully orelse you will be doomed

npoudel21: 2020-10-04 06:06:59

Isn't the sample answer wrong? Shouldn't the 14th term be 4/2
edit: My bad, I was mistaken on how the numbers are arranged in the list

Last edit: 2020-10-06 22:13:08
saurabh_shinde: 2020-09-10 15:57:29

easy in concept. just slight tricky to implement

coolboy7: 2020-06-04 18:26:11

Hint if you are not able to solve the problem:
Observe the pattern of numerator and denominator and also you need to apply the formula of first n terms;)

manish_thakur: 2019-12-12 12:28:09

position(x,y) = (1/2)(x+y)(x+y+1) + y

gak: 2019-10-28 10:53:57

Observe the pattern by summing numerator and denominator, after that it's a cakewalk.

saraswat000: 2019-08-27 21:08:22

AC in one go!

mriow: 2019-08-20 09:02:27

Solution can be achieved in O(1) for every Cantor's Term.

Hint:

Use the formula for the Sum of the First n Terms of an Arithmetic Sequence.


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