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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

A rational number is a number that can be expressed as the fraction p/q of two integers. We are going to describe a Number System which covers rational numbers.We start with two

**seeds**of rational numbers: 0/1 and 1/0.

ðŸ‘‰ 0/1 is zero. In this context it is the

ðŸ‘‰ 1/0 is usually undefined and causes error in computing. But now we define it to be the

Then, we find the

**mediant**of the two extreme seeds.

ðŸ‘‰ The mediant of a/b and c/d is defined as (a+c)/(b+d).

Insert the mediant in between.

0/1 1/0

0/1 (1/1) 1/0

0/1 (1/2) 1/1 (2/1) 1/0

For every two adjacent terms, insert a mediant. The row will grow in length indefinitely.

We can represent these terms in a

**binary tree**.

ðŸ‘‰ The above row of numbers is the inorder-traversal of the binary tree.

0/1........... ,...........1/0

,~ 1/1 ~.

; :

; :

1/2 2/1

/ \ / \

1/3 2/3 3/2 3/1

/ \ / \ / \ / \

1/4 2/5 3/5 3/4 4/3 5/3 5/2 4/1

1/1 is the

**root**of the tree.

All rational numbers in the tree will not duplicate. All positive rational numbers in the Number System can be found somewhere in the tree. The tree itself is a Number System.

Using computer scientists' term, we use

**L**and

**R**to denote the left and right branches of a node in a binary tree. We specify a number by tracing its

**path**from the root.

**Some examples:**

3/5 is LRL

2/5 is LLR

8/5 is RLRL

**Tasks:**

You will be given some rational numbers. Translate them into L-R paths.

You will also be given some L-R paths. Translate them into the rational numbers as they are found in the tree.

ðŸ‘‰ All rational numbers in the tree are in reduced form. There is no 6/4 but there is 3/2.

ðŸ‘‰ To keep them as rational numbers, we do not simplify 2/1 into 2. We keep expressing it as a numerator and a denominator.

ðŸ‘‰ The two seeds and the root shall have special symbols other than L-R to represent them. In this puzzle we will not involve these special symbols.

ðŸ‘‰ Ref: https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree

Input

There will be multiple tests in each testcase.

By reading a line, you have to identify what kind of input it is. Then translate it into its equivalent representation of the other kind.

**Line 1:**An integer`N`for the number of tests to follow.**Following**Each line will be either a rational number in the form of`N`lines:`p/q`, or a path representation which is a string consisting of**L**and**R**By reading a line, you have to identify what kind of input it is. Then translate it into its equivalent representation of the other kind.

Output

**Write**

`N`lines:For each input line,

âœŽ write a L-R string if the input line is a rational number

âœŽ write a p/q rational number if the input line is a L-R string

Constraints

1 â‰¤

1 â‰¤ length of L-R string â‰¤ 2000

`p`,`q`â‰¤ 5,000,000,000,000,0001 â‰¤ length of L-R string â‰¤ 2000

Example

Input

5 3/5 2/5 8/5 LRL RLRL

Output

LRL LLR RLRL 3/5 8/5

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