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Given "①②③④⑤⑥⑦⑧⑨⑩⑪⑫" as plain text and a 4 rows Scytale inscription with 3 as the length of the longest row, the original plaintext is back after 5 runs:

①④⑦⑩②⑤⑧⑪③⑥⑨⑫

①⑩⑧⑥④②⑪⑨⑦⑤③⑫

①⑥⑪⑤⑩④⑨③⑧②⑦⑫

①⑤⑨②⑥⑩③⑦⑪④⑧⑫

①②③④⑤⑥⑦⑧⑨⑩⑪⑫

Given "Juliet is still alive!!!" as plain text and a 4 rows Scytale inscription with 6 as the length of the longest row, the original plaintext is back after 11 runs:

J iiuilvlslei !esa!ttl!

Jlia v !il tis!tulelies!

J iel!slii!ialte usvtl!

Jsau llsiitveietl! l!i !

Jle ssilaie!uiti tl lv!!

Jiullli eatl iivse !s!t!

Ji i i!ueislav!ltstlle!

Jilsi!at uvl e!liile st!

Ja liteel ! sulsivit!li!

Jesiaeut ll!l sli!iit v!

Juliet is still alive!!!

So, my question is: how to determine the number of runs until the ciphertext matches the plain text without having to run them and testing for the match at each run?

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