CF1081B.Farewell Party

Chouti and his classmates are going to the university soon. To say goodbye to each other, the class has planned a big farewell party in which classmates, teachers and parents sang and danced.

Chouti remembered that $n$ persons took part in that party. To make the party funnier, each person wore one hat among $n$ kinds of weird hats numbered $1, 2, \ldots n$. It is possible that several persons wore hats of the same kind. Some kinds of hats can remain unclaimed by anyone.

After the party, the $i$-th person said that there were $a_i$ persons wearing a hat differing from his own.

It has been some days, so Chouti forgot all about others' hats, but he is curious about that. Let $b_i$ be the number of hat type the $i$-th person was wearing, Chouti wants you to find any possible $b_1, b_2, \ldots, b_n$ that doesn't contradict with any person's statement. Because some persons might have a poor memory, there could be no solution at all.

Chouti 和他的同学们即将升入大学。为了彼此告别，班级举办了一场盛大的欢送会，同学们、老师和家长们纷纷载歌载舞。

Chouti 记得当时共有 $n$ 人参加了这场欢送会。为了让晚会更有趣，每人戴了一顶帽子，帽子共有 $n$ 种奇特的款式，编号为 $1, 2, \ldots, n$。多人可能戴了同款帽子，也可能有某些款式的帽子无人佩戴。

晚会结束后，第 $i$ 个人声称：有 $a_i$ 个人所戴的帽子与他自己的不同。

如今已过去数日，Chouti 已完全记不清其他人所戴帽子的款式，但他对此很好奇。设 $b_i$ 表示第 $i$ 个人所戴帽子的款式编号，Chouti 希望你找出任意一组满足所有人陈述的 $b_1, b_2, \ldots, b_n$。由于部分人可能记性不好，该问题也可能无解。

The first line contains a single integer $n$ ($1 \le n \le 10^5$), the number of persons in the party.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le n-1$), the statements of people.

第一行包含一个整数 $n$（$1 \le n \le 10^5$），表示派对中的人数。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le n-1$），表示每个人的陈述。

If there is no solution, print a single line "Impossible".

Otherwise, print "Possible" and then $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \le b_i \le n$).

If there are multiple answers, print any of them.

如果没有解，输出一行 "Impossible"。

否则，输出 "Possible"，然后输出 $n$ 个整数 $b_1, b_2, \ldots, b_n$（其中 $1 \le b_i \le n$）。

如果存在多个答案，输出任意一个即可。

In the answer to the first example, all hats are the same, so every person will say that there were no persons wearing a hat different from kind $1$.

In the answer to the second example, the first and the second person wore the hat with type $1$ and all other wore a hat of type $2$.

So the first two persons will say there were three persons with hats differing from their own. Similarly, three last persons will say there were two persons wearing a hat different from their own.

In the third example, it can be shown that no solution exists.

In the first and the second example, other possible configurations are possible.

在第一个示例的答案中，所有帽子都相同，因此每个人都会说：没有人的帽子种类与第 $1$ 类不同。

在第二个示例的答案中，第一人和第二人戴的是第 $1$ 类帽子，其余所有人戴的都是第 $2$ 类帽子。

因此，前两人会说：有三人所戴帽子与其自身帽子种类不同；类似地，最后三人会说：有两人所戴帽子与其自身帽子种类不同。

在第三个示例中，可以证明不存在满足条件的解。

在第一个和第二个示例中，还可能存在其他可行的配置。