Clarence the Slow Typist Introduction

Clarence is a data entry clerk who works at an internet service provider. His job is to manually enter the IP addresses of all of the ISP's customers into the database. He does this using a keypad which has the following layout:

123
456
789
.0

The distance between the centre of horizontally or vertically adjacent keys is exactly one centimetre. For instance, the distance between the centres of 3 and 9 would be two centimetres. The distance between the centres of 3 and 5 would be √2cm. The Pythagoras theorem is sufficient to calculate the distance between any two keys.

Clarence, as you might expect from one who works in an ISP, uses a very slow and inefficient system of typing. He uses a single finger and searches for the key, and then moves his finger to the key, then presses it, and repeats for all of the digits in the number. You might know of this style as the "eagle search system" since the finger searches above the keyboard for the correct key before plunging down for the keypress, like an eagle plunging down for a kill.

For example, here is how Clarence would type out the number 7851:


He starts his finger at 7 and pushes the key.
He moves his finger to the right 1cm to 8 and pushes the key.
He moves his finger upwards 1cm to 5 and pushes the key.
He moves his finger diagonally upwards and left √2cm to 1 and pushes the key.


Therefore the total distance that Clarence moved his finger to type in 7851 is 1 + 1 + √2 which is about 3.41cm.

Your task is to write a program that calculates the distance Clarence must move his finger to type in arbitrary IP addresses. 

Input Description

Input is a string that will be in the form

().().().()

where each () is an integer in the range 0 - 999. This represents the IP address that Clarence must type in. An example input might be:

219.45.143.143

I would also like to point out that inputs such as 0.42.42.42 or 999.999.999.999 are still valid inputs, despite the fact that they are invalid IP addresses. So you don't need to include any IP address verification code in your program.

Output Description

Output the distance that Clarence must move his finger in order to type in the specified IP address. Round answers to two decimal places where needed, and use the cm unit in your output. The output for the example input is 27.38cm (1 + √8 + √5 + 2 + 1 + √5 + 3 + 1 + √5 + √13 + 3 + 1 + √5).
CJam, 46 44 43 38 37 34 bytes

rA,sd`f#3fmd2/2ew::.-::mh:+2mO"cm"


Thanks to @user23013 for suggesting mh, which made it possible to save 5 bytes.

Try it online in the CJam interpreter.

How it works

r     e# Read a token from STDIN.
A,    e# Push [0 1 2 3 4 5 6 7 8 9].
s     e# Stringify: [0 1 2 3 4 5 6 7 8 9] -&gt; "0123456789"
d     e# Cast to Double: "0123456789" -&gt; 123456789.0
`     e# Inspect: 123456789.0 -&gt; "123456789.0"
f#    e# Push the index of each character from the input in "123456789.0".
3fmd  e# Push the quotient and residue of each index divided by 3.
2/    e# Split the resulting array into pairs.
2ew   e# Convert the array of pairs in the array of all overlapping pairs of pair.
::.-  e# Reduce each pair using vectorized difference: [[a b][c d]] -&gt; [a-b c-d]
::mh  e# Reduce each reduced pair to its 2-norm distance: [a b] -&gt; sqrt(aa + bb)
:+    e# Sum all distances.
2mO   e# Round to two decimal places.
"cm"  e# Push "cm".