Namori Grundy

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.

Examples

Input

4 2 3 4 1

Output

POSSIBLE

Input

3 2 3 1

Output

IMPOSSIBLE

Input

4 2 3 1 1

Output

POSSIBLE

Input

6 4 5 6 5 6 4

Output

IMPOSSIBLE

inputFormat

Input

Input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

outputFormat

Output

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

Examples

Input

4 2 3 4 1

Output

POSSIBLE

Input

3 2 3 1

Output

IMPOSSIBLE

Input

4 2 3 1 1

Output

POSSIBLE

Input

6 4 5 6 5 6 4

Output

IMPOSSIBLE

样例

6
4 5 6 5 6 4

IMPOSSIBLE