Why are these cycles disjoint and of equal length?

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Hill
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TL;DR
In the conjugation of disjoint cycles, how do we know that the new cycles are also disjoint and of the same length as the original ones?
Given
1779973042144.webp


In the following derivation
1779973284930.webp

how do we know that
1779973351274.webp

?
 

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