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Given a permutation $\pi:[n]\to[n]$ of cards from $1$ to $n$ you can find the first card to move to the front the following way:

1. $c \leftarrow n$
2. for each $k$ from $n$ down to $1$ do
3. $\space\space\space$ if $c = \pi(k)$ then
4. $\space\space\space\space\space\space$ $c \leftarrow c - 1$
5. $\space\space\space$ end if
6. end for
7. return $c$