Crypto Square

Implement the classic method for composing secret messages called a square code.

Given an English text, output the encoded version of that text.

First, the input is normalized: the spaces and punctuation are removed from the English text and the message is down-cased.

Then, the normalized characters are broken into rows.
These rows can be regarded as forming a rectangle when printed with intervening newlines.

For example, the sentence

"If man was meant to stay on the ground, god would have given us roots."

is normalized to:

"ifmanwasmeanttostayonthegroundgodwouldhavegivenusroots"

The plaintext should be organized into a rectangle as square as possible.
The size of the rectangle should be decided by the length of the message.

If c is the number of columns and r is the number of rows, then for the rectangle r x c find the smallest possible integer c such that:

• r * c >= length of message,
• and c >= r,
• and c - r <= 1.

Our normalized text is 54 characters long, dictating a rectangle with c = 8 and r = 7:

"ifmanwas"
"meanttos"
"tayonthe"
"groundgo"
"dwouldha"
"vegivenu"
"sroots  "

The coded message is obtained by reading down the columns going left to right.

The message above is coded as:

"imtgdvsfearwermayoogoanouuiontnnlvtwttddesaohghnsseoau"

Output the encoded text in chunks that fill perfect rectangles (r X c), with c chunks of r length, separated by spaces.
For phrases that are n characters short of the perfect rectangle, pad each of the last n chunks with a single trailing space.

"imtgdvs fearwer mayoogo anouuio ntnnlvt wttddes aohghn  sseoau "

Notice that were we to stack these, we could visually decode the ciphertext back in to the original message:

"imtgdvs"
"fearwer"
"mayoogo"
"anouuio"
"ntnnlvt"
"wttddes"
"aohghn "
"sseoau "