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