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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

string solve() {
  int N;
  cin >> N;
  vector<vector<int>> G(N);
  for(auto i=0; i<N; ++i) {
    int p;
    cin >> p;
    G[p-1].emplace_back(i);
  }

  vector<int> Grundy(N, -1);

  function<int(int, int)> dfs = [&](auto u, auto d) {
    if(Grundy[u]!=-1) return Grundy[u];
    Grundy[u] = N;
    set<int> S;
    for(auto v: G[u]) S.emplace(dfs(v, d));
    for(auto i=0; i<N; ++i) if(!S.count(i)) if(!S.count(N) || d--==0) return Grundy[u] = i;
    assert(false);
  };

  auto check = [&]() {
    for(auto u=0; u<N; ++u) {
      set<int> S;
      for(auto v: G[u]) {
        if(Grundy[u]==Grundy[v]) return false;
        S.emplace(Grundy[v]);
      }
      for(auto i=0; i<Grundy[u]; ++i) if(!S.count(i)) return false;
    }
    return true;
  };

  for(auto d: {0, 1}) {
    Grundy.assign(N, -1);
    for(auto v=0; v<N; ++v) dfs(v, d);
    if(check()) return "POSSIBLE";
  }
  return "IMPOSSIBLE";
}

int main() {
  cout << solve() << endl;
}