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 <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <map>
#include <list>
#include <set>
#include <numeric>
#include <queue>
#include <stack>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <climits>
#include <cfloat>
#include <ctime>
#include <complex>
#include <cassert>
#include <array>
#include <bitset> 
#include <unordered_map>
#include <random>

using namespace std;
typedef long long LL;
typedef pair<int,int> P;

const int L=200*1000+1;
int p[L];
vector<int> edge[L];
bool done[L];
vector<int> order,order1;
void dfs(int i){
	done[i]=false;
	for(auto j:edge[i]){
		if(done[j]){
			dfs(j);
		}
	}
	order.push_back(i);
}
void dfs1(int i){
	done[i]=true;
	if(!done[p[i]]){
		dfs1(p[i]);
	}
	order1.push_back(i);
}

int a[L];
int main() {
	int N;
	scanf("%d",&N);
	for(int i=1;i<=N;i++){
		scanf("%d",p+i);
		edge[p[i]].push_back(i);
	}
	for(int i=1;i<=N;i++){
		if(!done[i]){
			dfs1(i);
		}
	}
	reverse(order1.begin(),order1.end());
	for(auto i:order1){
		if(done[i]){
			dfs(i);
		}
	}
	
	//reverse(order.begin(),order.end());
	/*
	for(auto i:order){
		cerr << i << endl;
	}
	*/
	for(int t=0;t<2;t++){
		memset(a,0,sizeof(a));
		int f=-1;
		for(auto i:order){
			vector<int> v;
			for(int k:edge[i]){
				if(a[k]==0){
					f=i;
				}
				else{
					v.push_back(a[k]);
				}
			}
			sort(v.begin(),v.end());
			int w=0;
			for(int q:v){
				if(w+1<q){
					break;
				}
				w=q;
			}
			if(f==i){
				a[i]=w+1+t;
			}
			else{
				a[i]=w+1;
			}
			//cerr << i << ": " << a[i] << endl;
		}
		//cerr << "# " << f << endl;
		if(t==0){
			if(a[f]!=a[order.back()]){
				puts("POSSIBLE");
				return 0;
			}
		}
		else{
			if(a[order.back()]+1==a[f]){
				puts("POSSIBLE");
				return 0;
			}
		}
	}
	puts("IMPOSSIBLE");

	return 0;
}