Permutation into chained transpositions?

Question

I know that every permutation can be factored as a product of transpositions.

I wonder if every permutation can be factored as product of chained transpositions ?

For example

[5,1,3,0,4,2] = [(3,2),(2,5),(5,0)]
                    \__/  \__/

And, if so, starting with an arbitrary element ?

Answer 1

Hint: The product of chained transpositions is always a cycle.