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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

Picture yourself as an intrepid intergalactic navigator, entrusted with the task of charting a course through a mesmerizing cosmic wormhole. Your advanced ship is equipped with cutting-edge sensors capable of detecting vectors representing the elusive location of this celestial phenomenon. You'll be provided with two vectors, denoted as`ship`and

`wormhole`, the magnitude of each component (i,j,k) being integers.

To guarantee a secure passage through this ethereal expanse, you must develop a program that can precisely calculate the

**direction**and

**distances**between your ship and the wormhole. However, there's a twist! The sensors have encountered an unexpected glitch, introducing superfluous white spaces between coordinates. Furthermore, they may not adhere to the conventional

**i**,

**j**, and

**k**sequence. For instance, you might receive a vector like

**"2i-3k+4j"**, where the default

**i, j and k**sequence is violated.

Additionally, if no number is explicitly mentioned before a component, consider it to be 1. For instance,

**"k+i-j"**equates to

**"1k+1i-1j"**. And if a component is entirely absent, its value is assumed to be 0, like

**"i-k"**, which is equivalent to

**"1i+0j-1k"**.

**Hint:**

1) The vector ai+bj+ck denotes the coordinates (a,b,c) in space

2) Distance between two points (say (a1,b1,c1) and (a2,b2,c2)) is calculated by √((a2 – a1)² + (b2 – b1)² + (c2-c1)²)

3) Directional vector of one vector(a1i+b1j+c1k) with respect to another vector(a2i+b2j+c2k) is given by (a1-a2)i+(b1-b2)j+(c1-c2)k

4) The sign before the first component of directional vector is omitted if it is positive. That is,

**+2i+3j-4k**should be written as

**2i+3j-4k**, whereas

**-9i+8j+4k**remains the same.

5) Return the directional vectors in their simplified form by dividing each component by the GCD (Greatest Common Divisor) of the components. That is,

**2i-4j**should be converted to

**i-2j**

6) Finally, round the distance off to 2 decimal places.

Prepare for a cosmic challenge, Captain! It's time to navigate through the wormhole with finesse and precision.

Input

**Line 1:**A string

`ship`representing the location of the ship in space.

**Line 2:**A string

`wormhole`representing the location of the wormhole in space.

Output

**Line 1:**The directional vector to the wormhole from the ship

**Line 2:**Distance between the ship and the wormhole rounded off to two decimal places.

Constraints

1 ≤ length(

1 ≤ length(

`ship`) ≤ 201 ≤ length(

`wormhole`) ≤ 20Example

Input

i+j-k i-j+k

Output

Direction: -j+k Distance: 2.83

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