200793: [AtCoder]ARC079 F - Namori Grundy

Problem Statement

There is a directed graph with $N$ vertices and $N$ edges. The vertices are numbered $1, 2, ..., N$.

The graph has the following $N$ edges: $(p_1, 1), (p_2, 2), ..., (p_N, N)$, and the graph is weakly connected. Here, an edge from Vertex $u$ to Vertex $v$ is denoted by $(u, v)$, and a weakly connected graph is a graph which would be connected if each edge was bidirectional.

We would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, $a_i$ is the value assigned to Vertex $i$.

• Each $a_i$ is a non-negative integer.
• For each edge $(i, j)$, $a_i \neq a_j$ holds.
• For each $i$ and each integer $x(0 ≤ x < a_i)$, there exists a vertex $j$ such that the edge $(i, j)$ exists and $x = a_j$ holds.

Determine whether there exists such an assignment.

Constraints

• $2 ≤ N ≤ 200$ $000$
• $1 ≤ p_i ≤ N$
• $p_i \neq i$
• The graph is weakly connected.

Input

Input is given from Standard Input in the following format:

$N$
$p_1$ $p_2$ ... $p_N$

Output

If the assignment is possible, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

4
2 3 4 1

Sample Output 1

POSSIBLE

The assignment is possible: {$a_i$} = {$0, 1, 0, 1$} or {$a_i$} $=$ {$1, 0, 1, 0$}.

Sample Input 2

3
2 3 1

Sample Output 2

IMPOSSIBLE

Sample Input 3

4
2 3 1 1

Sample Output 3

POSSIBLE

The assignment is possible: {$a_i$} $=$ {$2, 0, 1, 0$}.

Sample Input 4

6
4 5 6 5 6 4

Sample Output 4

IMPOSSIBLE