How to express $(142536)$ as string of $(13456)$ and $(132)$ in $S_6$?

Question

Suppose that $r=(13456)$ and $s=(132)$ be two permutations in $S_6,$ the group of all permutations of the symbols in $\{1,2,3,4,5,6\}$.

Let $\alpha=(142536)$. I am willing to express $\alpha$ as a string of $r,s$ as $$\alpha=r^{m_1}s^{m_2}r^{m_3}s^{m-4}\cdots$$
where $m_1, m_2, \cdots$ will be integers.

I do not know if there is any general procedure to determine $m_1, m_2, \cdots$ manually.

If any such method exists, please share the link or please tell me how to solve it.

Thanks in advance. Please feel free to edit my question if necessary

Answer 1

You can't do this at all. $(142536)$ is an odd permutation, so you cannot write it in terms of even permutations $(13456)$ and $(132)$. Any product of even permutations is itself even.