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 $a$.

Alice 是一位魔术师，她设计了一个新魔术。她有 $n$ 张卡片，每张卡片上分别写有一个从 $1$ 到 $n$ 的不同数字。首先，她请一位观众将这副牌洗匀，并将卡片排成一行。设从左往右数第 $i$ 张卡片上的数字为 $a_i$。

接着，Alice 选择两个排列 $p$ 和 $q$。对 $p$ 和 $q$ 有一个限制条件：这两个排列都不能有不动点，即对所有 $i$，均需满足 $p_i \ne i$ 且 $q_i \ne i$。

选定排列后，Alice 按照它们对卡片进行洗牌。洗牌后，从左往右数第 $i$ 张卡片，是原先排列中编号为 $a[p[q[i]]$ 的卡片（即：先应用 $q$，再应用 $p$，最后取 $a$ 中对应位置的值）。若洗牌后从左往右数第 $i$ 张卡片上的数字恰好为 $i$，则该魔术视为成功。

请帮助 Alice 找出满足条件的排列 $p$ 和 $q$；若对给定的初始排列 $a$ 不存在这样的排列，请说明其不可能性。

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 $10^5$.

输入的第一行包含测试用例的数量 $t$（$1 \leq t \leq 10^5$）。

每个测试用例由两行描述。第一行包含一个整数 $n$ —— 卡片的数量（$1 \leq n \leq 10^5$）。第二行包含 $n$ 个整数 $a_i$ —— 卡片的初始排列（$1 \leq a_i \leq n$；$\forall i \neq j: a_i \neq a_j$）。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

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 $q$.

按输入中测试用例出现的相同顺序，为每个测试用例输出答案。

对于每个测试用例，若不存在解，则在单独一行中输出 "Impossible"。

否则，在第一行输出 "Possible"，并在接下来的两行中分别输出排列 $p$ 和 $q$。