A. Amazing Tricktime limit per test3 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputAlice 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. InputThe 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.OutputPrint 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.ExampleInput
422 131 2 342 1 4 355 1 4 2 3Output
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

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 
['constructive algorithms', 'graph matchings', 'math', 'probabilities', '*1900']