A15616 | 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 $q$ — 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 "Impossible" in a single line, if no solution exists.

Otherwise, print "Possible" in the first line, and in the following two lines print permutations $p$ and $q$ .