#include<bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
#define ld long double
#define F first
#define S second

using namespace :: std;

const ll maxn=2e5+500;
const ll mod=1e9+7;
const ll inf=1e9+500;

ll in[maxn];
bool vis[maxn];
ll y;
bool dor[maxn];
bool barg[maxn];
ll anss[maxn];
vector<ll> out[maxn];



void  dfs(ll a){
	if(vis[a]){
		y=a;
		return ;
	}
	vis[a]=1;
	dfs(in[a]);
}
void dfss(ll a){
	if(dor[a]){
		return;
	}
	dor[a]=1;
	dfss(in[a]);
}
ll mexx(ll a){
	vector<ll> b;
	for(ll i=0;i<out[a].size();i++){
		b.pb(anss[out[a][i]]);
	}
	sort(b.begin(),b.end());
	ll ans=0;
	for(ll i=0;i<b.size();i++){
		if(b[i]==ans){
			ans++;
		}
	}
	return ans;
}
void dfsw(ll a){
	for(ll i=0;i<out[a].size();i++){
		dfsw(out[a][i]);
	}
	anss[a]=mexx(a);
}
void dfse(ll a){
	vis[a]=1;
	ll v=in[a];
	if(vis[v]){
		return ;
	}
	anss[v]=mexx(v);
	dfse(v);
}
bool good(ll n){
	for(ll i=0;i<n;i++){
		if(mexx(i)!=anss[i]){
			return 0;
		}
	}
	return 1;
}
int main(){
	ll n;
	cin>>n;
	for(ll i=0;i<n;i++){
		cin>>in[i];
		in[i]--;
		out[in[i]].pb(i);
	}
	dfs(0);
	dfss(y);
	for(ll i=0;i<n;i++){
		barg[in[i]]=1;
	}
	for(ll i=0;i<n;i++){
		barg[i]=!barg[i];
	}
	for(ll i=0;i<n;i++){
		if(dor[i]){
			for(ll j=0;j<out[i].size();j++){
				ll v=out[i][j];
				if(dor[v]==0){
					dfsw(v);	
				}
			}
		}
	}
	for(ll i=0;i<40;i++){
		fill(vis,vis+maxn,0);
		anss[y]=i;
		dfse(y);
		if(good(n)){
			cout<<"POSSIBLE";
			return 0;
		}
	}
	cout<<"IMPOSSIBLE";
}

### Prompt

Generate 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>
#define ll long long
#define pb push_back
#define mp make_pair
#define ld long double
#define F first
#define S second

using namespace :: std;

const ll maxn=2e5+500;
const ll mod=1e9+7;
const ll inf=1e9+500;

ll in[maxn];
bool vis[maxn];
ll y;
bool dor[maxn];
bool barg[maxn];
ll anss[maxn];
vector<ll> out[maxn];



void  dfs(ll a){
	if(vis[a]){
		y=a;
		return ;
	}
	vis[a]=1;
	dfs(in[a]);
}
void dfss(ll a){
	if(dor[a]){
		return;
	}
	dor[a]=1;
	dfss(in[a]);
}
ll mexx(ll a){
	vector<ll> b;
	for(ll i=0;i<out[a].size();i++){
		b.pb(anss[out[a][i]]);
	}
	sort(b.begin(),b.end());
	ll ans=0;
	for(ll i=0;i<b.size();i++){
		if(b[i]==ans){
			ans++;
		}
	}
	return ans;
}
void dfsw(ll a){
	for(ll i=0;i<out[a].size();i++){
		dfsw(out[a][i]);
	}
	anss[a]=mexx(a);
}
void dfse(ll a){
	vis[a]=1;
	ll v=in[a];
	if(vis[v]){
		return ;
	}
	anss[v]=mexx(v);
	dfse(v);
}
bool good(ll n){
	for(ll i=0;i<n;i++){
		if(mexx(i)!=anss[i]){
			return 0;
		}
	}
	return 1;
}
int main(){
	ll n;
	cin>>n;
	for(ll i=0;i<n;i++){
		cin>>in[i];
		in[i]--;
		out[in[i]].pb(i);
	}
	dfs(0);
	dfss(y);
	for(ll i=0;i<n;i++){
		barg[in[i]]=1;
	}
	for(ll i=0;i<n;i++){
		barg[i]=!barg[i];
	}
	for(ll i=0;i<n;i++){
		if(dor[i]){
			for(ll j=0;j<out[i].size();j++){
				ll v=out[i][j];
				if(dor[v]==0){
					dfsw(v);	
				}
			}
		}
	}
	for(ll i=0;i<40;i++){
		fill(vis,vis+maxn,0);
		anss[y]=i;
		dfse(y);
		if(good(n)){
			cout<<"POSSIBLE";
			return 0;
		}
	}
	cout<<"IMPOSSIBLE";
}

```