Problem:
Score : 800 points

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

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as B
import qualified Data.IntSet as S
import qualified Data.Array.IArray as A
import qualified Data.Graph as G
import Data.Maybe
import Data.Bool

main = do
  n <- readLn
  ps <- map (fst . fromJust . B.readInt) . B.words <$> B.getLine
  let g = G.buildG (1,n) (zip ps [1..n])
  putStrLn $ bool "IMPOSSIBLE" "POSSIBLE" (namori n g)

namori n g = (odd n && p2) || (even n && (p1 || p2))
  where
    p1 = all even ds
    p2 = length (filter odd ds) == 2
    ds = zipWith (+) (A.elems (G.outdegree g)) (A.elems (G.indegree g))

type Vertex = Int
type Vertexes = S.IntSet
type Edge = (Vertex, Vertex)
type Graph = A.Array Vertex Vertexes

buildG :: Int -> [Edge] -> Graph
buildG n = A.accumArray (flip S.insert) S.empty (1, n)

size :: Graph -> Int
size = snd . A.bounds

from :: Graph -> Vertex -> Vertexes
from g = (g A.!)

degree :: Graph -> Vertex -> Int
degree g = S.size . (g A.!)

readDirectedEdge :: B.ByteString -> [Edge]
readDirectedEdge = map (constructOneWay . map readInt . B.words) . B.lines

constructOneWay :: [Int] -> Edge
constructOneWay [s,t] = (s, t)
constructOneWay _ = undefined

readInt :: B.ByteString -> Int
readInt = fst . fromJust . B.readInt