Score : 800 points
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.
Determine whether there exists such an assignment.
Input is given from Standard Input in the following format:
N p_1 p_2 ... p_N
If the assignment is possible, print POSSIBLE
; otherwise, print IMPOSSIBLE
.
4 2 3 4 1
POSSIBLE
The assignment is possible: {a_i} = {0, 1, 0, 1} or {a_i} = {1, 0, 1, 0}.
3 2 3 1
IMPOSSIBLE
4 2 3 1 1
POSSIBLE
The assignment is possible: {a_i} = {2, 0, 1, 0}.
6 4 5 6 5 6 4
IMPOSSIBLE