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

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

hide comments
2023-09-21 16:49:30
similar to:
https://www.spoj.com/problems/ZIGZAG/
for smallest number on nth diagonal see:
https://oeis.org/A152947
2021-03-19 04:01:11
GIVEN TEST CASE IS CORRECT
2021-01-16 17:25:49
HHAHA AC in one go
2020-11-08 08:19:10
check the output format carefully orelse you will be doomed
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
2020-09-10 15:57:29
easy in concept. just slight tricky to implement
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;)
2019-12-12 12:28:09
position(x,y) = (1/2)(x+y)(x+y+1) + y
2019-10-28 10:53:57
Observe the pattern by summing numerator and denominator, after that it's a cakewalk.
2019-08-27 21:08:22
AC in one go!
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