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)

const INF: usize = 1e15 as usize;

fn main() {
    let sc = std::io::stdin();
    let mut sc = Scanner { reader: sc.lock() };
    let n: usize = sc.read();
    let p: Vec<usize> = sc.read_vec(n);

    let mut graph = vec![vec![]; n];
    let mut inverted = vec![0; n];
    for i in 0..n {
        let from = p[i] - 1;
        let to = i;
        graph[from].push(to);
        inverted[to] = from;
    }

    let mut path = vec![];
    let mut visit = vec![false; n];
    let mut cur = (0..n).filter(|&i| graph[i].is_empty()).next().unwrap_or(0);
    path.push(cur);
    visit[cur] = true;
    loop {
        cur = inverted[cur];

        if visit[cur] {
            path = path
                .iter()
                .rev()
                .take_while(|&&v| v != cur)
                .map(|&v| v)
                .collect::<Vec<_>>();
            path.push(cur);
            break;
        }

        path.push(cur);
        visit[cur] = true;
    }

    let mut in_cycle = vec![false; n];
    for &p in path.iter() {
        in_cycle[p] = true;
    }
    let trees: Vec<Vec<usize>> = graph
        .iter()
        .map(|nexts| {
            nexts
                .iter()
                .filter(|&&next| !in_cycle[next])
                .map(|&next| next)
                .collect()
        })
        .collect();

    let mut num = vec![INF; n];
    for &c in path.iter() {
        dfs(c, &trees, &mut num);
    }
    adjust(&path, &mut num);
    for i in 0..n {
        if !validate(i, &graph, &mut num) {
            println!("IMPOSSIBLE");
            return;
        }
    }
    println!("POSSIBLE");
}

fn validate(v: usize, graph: &Vec<Vec<usize>>, num: &Vec<usize>) -> bool {
    let mut checked = vec![false; num[v]];
    for &next in graph[v].iter() {
        if num[next] == num[v] {
            return false;
        }
        if checked.len() < num[next] {
            continue;
        }
        checked[num[next]] = true;
    }
    checked.iter().all(|&b| b)
}

fn adjust(path: &Vec<usize>, num: &mut Vec<usize>) {
    let n = path.len();
    for i in (0..n).rev() {
        let (i, j) = (path[(n + i - 1) % n], path[i]);
        if num[i] == num[j] {
            num[i] += 1;
        }
    }
}

fn dfs(v: usize, graph: &Vec<Vec<usize>>, num: &mut Vec<usize>) {
    if graph[v].is_empty() {
        num[v] = 0;
        return;
    }
    for &next in graph[v].iter() {
        dfs(next, graph, num);
    }
    let mut nexts = graph[v].iter().map(|&next| num[next]).collect::<Vec<_>>();
    nexts.sort();
    let mut cur = 0;
    for &next in nexts.iter() {
        if cur == next {
            cur += 1;
        } else if cur < next {
            num[v] = cur;
            return;
        }
    }
    num[v] = cur;
}

pub struct Scanner<R> {
    reader: 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
            .reader
            .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 read_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()
    }
}