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
2018-01-29 09:44:14
AC in 1 go, 0.00 sec
2018-01-23 01:05:47
LOL memory limit allows you to store 2d array
2018-01-19 17:08:02
AC in a go!
2017-12-22 14:00:49
ac in one go!!!
2017-12-08 08:05:45
AC in 1 GO.
2017-11-15 15:04:53
O(1)
2017-10-23 21:18:02
AC in one go.....one should first observe d pattern..if want to make a formula,try to observe num nd den...

Last edit: 2017-10-23 21:18:32
2017-10-21 21:00:44
the corners..........
2017-09-27 20:22:20
Very nice problem. AC in one go.
2017-08-17 11:51:59
took 5 hours to solve it.
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