2022-2023 ICPC, NERC, Northern Eurasia Onsite (Unrated, Online Mirror, ICPC Rules, Teams Preferred) |
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Finished |
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 $$$q$$$.
422 131 2 342 1 4 355 1 4 2 3
Impossible Possible 3 1 2 2 3 1 Possible 3 4 2 1 3 4 2 1 Possible 4 1 2 5 3 3 1 4 5 2
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