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

bool incycle[200000];
vector<int> edge[200000];
int visit[200000];
int val[200000];
bool dfs(int x,int p){
	visit[x]=1;
	for(int i:edge[x])
		if(visit[i]==1){
			incycle[x]=true;
			visit[x]=2;
			return true;
		}
		else if(visit[i]==0)
			if(dfs(i,x)){
				incycle[x]=true;
				visit[x]=2;
				return true;
			}
	visit[x]=2;
	return false;
}

void dfs2(int x){
	set<int> tmp;
	for(int i:edge[x]){
		if(!incycle[i])
			dfs2(i),tmp.insert(val[i]);
	}
	for(int i=0;;i++)
		if(tmp.find(i)==tmp.end()){
			val[x]=i;
			break;
		}
}
set<int> s;

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	for(int i=0,p;i<n;i++){
		cin>>p;
		p--;
		edge[p].emplace_back(i);
	}
	for(int i=0;i<n;i++)
		if(!visit[i])
			dfs(i,-1);
	int cnt=0;
	for(int i=0;i<n;i++)
		if(incycle[i])
			dfs2(i),s.insert(val[i]),cnt++;
	if(s.size()!=1||cnt%2==0)
		cout<<"POSSIBLE"<<endl;
	else
		cout<<"IMPOSSIBLE"<<endl;
	
}

### Prompt

Please formulate a cpp solution to the following problem:

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`.

Examples

Input

4
2 3 4 1


Output

POSSIBLE


Input

3
2 3 1


Output

IMPOSSIBLE


Input

4
2 3 1 1


Output

POSSIBLE


Input

6
4 5 6 5 6 4


Output

IMPOSSIBLE

### Response

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

bool incycle[200000];
vector<int> edge[200000];
int visit[200000];
int val[200000];
bool dfs(int x,int p){
	visit[x]=1;
	for(int i:edge[x])
		if(visit[i]==1){
			incycle[x]=true;
			visit[x]=2;
			return true;
		}
		else if(visit[i]==0)
			if(dfs(i,x)){
				incycle[x]=true;
				visit[x]=2;
				return true;
			}
	visit[x]=2;
	return false;
}

void dfs2(int x){
	set<int> tmp;
	for(int i:edge[x]){
		if(!incycle[i])
			dfs2(i),tmp.insert(val[i]);
	}
	for(int i=0;;i++)
		if(tmp.find(i)==tmp.end()){
			val[x]=i;
			break;
		}
}
set<int> s;

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	for(int i=0,p;i<n;i++){
		cin>>p;
		p--;
		edge[p].emplace_back(i);
	}
	for(int i=0;i<n;i++)
		if(!visit[i])
			dfs(i,-1);
	int cnt=0;
	for(int i=0;i<n;i++)
		if(incycle[i])
			dfs2(i),s.insert(val[i]),cnt++;
	if(s.size()!=1||cnt%2==0)
		cout<<"POSSIBLE"<<endl;
	else
		cout<<"IMPOSSIBLE"<<endl;
	
}

```