P12790 [NERC 2022] Amazing Trick

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 $q$ --- $\textbf{permutations can't have fixed points}$. 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 $a$.

The first line of the input contains the number of tests $t$ ($1 \leq t \leq 10^5$). Each test is described in two lines. The first line contains one integer $n$ --- the number of cards ($1 \leq n \leq 10^5$). The second line contains $n$ integers $a_i$ --- the initial permutation of the cards ($1 \leq a_i \leq n$; $\forall i \neq j: a_i \neq a_j$). It is guaranteed that the sum of $n$ over all tests does not exceed $10^5$.

Print the answer for each test case in the same order the cases appear in the input. For each test case, print $\tt{Impossible}$ in a single line, if no solution exists. Otherwise, print $\tt{Possible}$ in the first line, and in the following two lines print permutations $p$ and $q$.