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 Rust (1.42.0) (judge verdict: Accepted)

use std::collections::{BTreeSet, VecDeque};

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let mut graph = vec![vec![]; n];
    let mut parent = vec![0; n];
    for i in 0..n {
        let p = sc.read::<usize>() - 1;
        graph[p].push(i);
        parent[i] = p;
    }

    let mut q = VecDeque::new();
    let mut a = vec![-1; n];
    for i in 0..n {
        let is_leaf = graph[i].is_empty();
        if is_leaf {
            q.push_back(i);
            a[i] = 0;
        }
    }

    let mut reach = vec![0; n];
    while let Some(v) = q.pop_front() {
        let parent = parent[v];
        reach[parent] += 1;
        if reach[parent] == graph[parent].len() {
            let children = graph[parent]
                .iter()
                .map(|&child| a[child])
                .collect::<BTreeSet<_>>();
            a[parent] = (0..).find(|&a| !children.contains(&a)).unwrap();
            q.push_back(parent);
        }
    }

    let v = (0..n).find(|&i| a[i] == -1).unwrap();
    let v_children = graph[v]
        .iter()
        .filter(|&&i| a[i] != -1)
        .map(|&i| a[i])
        .collect::<BTreeSet<_>>();
    let candidates = (0..)
        .filter(|&i| !v_children.contains(&i))
        .take(2)
        .collect::<Vec<_>>();

    for candidate in candidates.into_iter() {
        a[v] = candidate;
        let mut cur = parent[v];
        while cur != v {
            let children = graph[cur].iter().map(|&i| a[i]).collect::<BTreeSet<_>>();
            a[cur] = (0..).find(|&i| !children.contains(&i)).unwrap();
            cur = parent[cur];
        }
        let check = graph[v].iter().map(|&i| a[i]).collect::<BTreeSet<_>>();
        if (0..).find(|&i| !check.contains(&i)).unwrap() == a[v] {
            println!("POSSIBLE");
            return;
        }
    }
    println!("IMPOSSIBLE");
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write_all(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}