Alice is a magician and she creates a new trick. She has cards with different numbers from to written on them. First, she asks an audience member to shuffle the deck and put cards in a row. Let’s say the -th card from the left has the number on it.
Then Alice picks two permutations and . There is a restriction on and — permutations can’t have fixed points. Which means and .
After permutations are chosen, Alice shuffles the cards according to them. Now the -th card from the left is the card . The trick is considered successful if -th card from the left has the number on it after the shuffles.
Help Alice pick the permutations and or say it is not possible for the specific starting permutation .
The first line contains the number of tests .
Each test is described in two lines. The first line contains one integer — the number of cards. The second line contains integers — the initial permutation of the cards.
It is guaranteed that the sum of over all tests does not exceed .
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 and .