## NG0FRCTN - Fractions on Tree

A fraction tree is an infinite binary tree defined as follows:

1) Every node of tree contains a fraction

2) Root of tree contains the fraction 1/1

3) Any node with fraction i/j has two children : left child with fraction i/(i+j) and right child with fraction (i+j)/j

For example , fraction tree upto 3 levels is as shown:

We number the nodes according to increasing levels ( root is at level 1) and at any same level , nodes are numbered from left to right. So first node holds the fraction 1/1 , second one holds 1/2 , third one holds 2/1 fourth one holds 1/3 and so on.

Your task is simple. Given a number n , you are to find the fraction at the nth node.

### Input

Every line of the input contains a single number n. You are to find the fraction at nth node of fraction tree. Input file terminates with a 0 which is not to be processed.

### Output

For each input , print numerator and denominator of the lowest form of the fraction seperated by a /. Output of each case to be done in seperate lines.

### Example

```Input:
1
2
3
7
0

Output:
1/1
1/2
2/1
3/1```

### Constraints

1 <= # of test cases <= 30000, 1 <= N <= 10^10

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 < Previous 1 2 Next > spoj2121: 2015-12-01 13:53:22 try for a O(T*logn) solution its is easy to implement krish: 2015-04-22 12:57:01 10000000000 ans:7271/77695 10^8 ans:897/7901 Francky: 2014-12-29 16:00:53 (29/12/2014) Image uploaded, and now visible. Martijn Muijsers: 2013-10-18 13:25:03 Tested all possible cases with Wolfram API, all correct. Getting wrong answer :S Could you possibly check 10287391? :) Sidharth Guglani: 2012-08-29 22:41:31 getting WA don't know why passing all the test cases on the forum. please check my solution id 7557575 EDIT : ACC.. Last edit: 2013-01-30 06:13:08 Shubham: 2012-08-22 17:19:28 too tough in python :\ the problem would be tricky if initially it were not 1/1 well i am lagging: 2012-02-06 18:01:18 image is not visible please fix the problem Santiago Palacio: 2012-01-09 22:02:33 Image is not really necessary, i believe. Ajey Golsangi: 2012-01-05 10:12:55 Image not visible. Please correct the problem. [Retired] Fendy Kosnatha: 2011-03-29 02:41:53 image is visible, please updated...

 Added by: Nikhil Garg Date: 2009-12-19 Time limit: 1.440s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: NODEJS OBJC PERL6 SQLITE VB.NET Resource: own