Alice is a magician and she creates a new trick. She has $n$ cards with different numbers from $1$ to $n$ written on them. First, she asks an audience member to shuffle the deck and put cards in a row. Let's say the $i$-th card from the left has the number $a_i$ on it.

Then Alice picks two permutations $p$ and $q$. There is a restriction on $p$ and $q$ — permutations can't have fixed points. Which means $\forall i: p_i \ne i\ and\ q_i \ne i$.

After permutations are chosen, Alice shuffles the cards according to them. Now the $i$-th card from the left is the card $a[p[q[i]]$. The trick is considered successful if $i$-th card from the left has the number $i$ on it after the shuffles.

Help Alice pick the permutations $p$ and $q$ or say it is not possible for the specific starting permutation $a$.