CF1773A 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 $ .