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 (1.15.1) (judge verdict: Wrong Answer)

use std::collections::BTreeSet;

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let p: Vec<usize> = (0..n).map(|_| sc.read::<usize>() - 1).collect();
    let mut graph = vec![vec![]; n];
    for (i, &p) in p.iter().enumerate() {
        graph[p].push(i);
    }

    let mut vis = vec![false; n];
    let mut cur = 0;
    while !vis[cur] {
        vis[cur] = true;
        cur = p[cur];
    }

    let mut in_cycle = vec![false; n];
    while !in_cycle[cur] {
        in_cycle[cur] = true;
        cur = p[cur];
    }

    let mut grundy = vec![n; n];
    for i in in_cycle.iter().enumerate().filter(|&(_, &in_cycle)| in_cycle).map(|(i, _)| i) {
        for &child in graph[i].iter() {
            if !in_cycle[child] {
                dfs(child, &graph, &mut grundy);
            }
        }
    }

    let check = |first: usize, grundy: &mut Vec<usize>| -> bool{
        let mut cur = p[first];
        loop {
            let set = graph[cur].iter().map(|&next| grundy[next]).collect::<BTreeSet<usize>>();
            let g = (0..).filter(|i| !set.contains(i)).next().unwrap();

            if cur == first {
                if g == grundy[first] {
                    return true;
                } else {
                    return false;
                }
            } else {
                grundy[cur] = g;
                cur = p[cur];
            }
        }
    };

    let first = cur;
    let set = graph[first].iter().map(|&next| grundy[next]).collect::<BTreeSet<usize>>();
    let mut iter = (0..).filter(|i| !set.contains(i));
    let candidate1 = iter.next().unwrap();
    grundy[first] = candidate1;
    if check(first, &mut grundy) {
        println!("POSSIBLE");
        return;
    }


    let candidate2 = iter.next().unwrap();
    grundy[first] = candidate2;
    if check(first, &mut grundy) {
        println!("POSSIBLE");
        return;
    }
    println!("IMPOSSIBLE");
}

fn dfs(v: usize, graph: &Vec<Vec<usize>>, grundy: &mut Vec<usize>) -> usize {
    let n = grundy.len();
    if grundy[v] != n {
        return grundy[v];
    }
    let set = graph[v].iter().map(|&child| grundy[child]).collect::<BTreeSet<usize>>();
    grundy[v] = (0..).filter(|i| !set.contains(i)).next().unwrap();
    grundy[v]
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .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()
    }
}