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
Santiago Palacio: 2011-05-30 19:39:32

What do you not understand from the diagram? they're just going through the diagram in zig-zag

HELLO: 2011-02-09 06:46:29

diagram is not clear

Ales Tamchyna: 2010-02-15 08:33:29

@Sai Ganesh
2/17 is the 17-th element in the 2nd row, 3/19 is the 19-th element in the 3rd row.

Shanky: 2009-12-01 13:45:25

You can view above diag. as pascal's triangle and then find the nth term by moving in an zigzag manner

Sai Ganesh: 2009-10-04 12:33:58

The given diagram is not very clear..does the above diagram mean there is no number for fractions like 2/17 , 3/19 and so on?


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