Amazing Trick

题意翻译

给定一个排列 $a_{1\sim n}$，请你求出两个排列 $p_{1\sim n}$ 和 $q_{1\sim n}$，使 $a'_i=a_{p_{q_i}}$，得到的新排列 $a'_{1\sim n}$ 满足 $a'_i=i$，但由于一些特殊的原因，你需要保证 $p_i\not=i$ 且 $q_i\not=i$。若无解则输出 `Impossible`，有解则输出 `Possible` 并输出 $p$ 和 $q$。

题目描述

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 $ .

输入输出格式

输入格式

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 $ .

输出格式

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 $ .

输入输出样例

输入样例 #1

4
2
2 1
3
1 2 3
4
2 1 4 3
5
5 1 4 2 3

输出样例 #1

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