#include "bits/stdc++.h"
#define ll long long
#define rep2(i,a,b) for(int i=a;i<=b;++i)
#define rep(i,n) for(int i=0;i<n;i++)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define tii tuple<int,int,int>
#define pq priority_queue<int>
#define pqg priority_queue<int,vector<int>,greater<int>>
#define pb push_back
#define edge(v,a,b) v[a].pb(b);v[b].pb(a);
ll MOD=998244353;
#define INF 2*1e9
#define N 600010
#define MAX_V 900010
using namespace std;
int visited[N],num[N];
int mem,p[N],s;
vector<int> G[N];
int dfs(int x){
    vector<int> v;
    rep(i,G[x].size()){
        if(G[x][i]==mem)continue;
        v.pb(dfs(G[x][i]));
    }
    sort(v.begin(),v.end());
    if(v.size()==0){
        return num[x]=0;
    }
    int a=-1;
    rep(i,v.size()){
        if(v[i]==a+1){a++;continue;}
        if(v[i]==a){continue;}
        break;
    }
    a++;
    return num[x]=a;
}
int dfs2(int x){
    vector<int> v;
    rep(i,G[x].size()){
        if(G[x][i]==mem)continue;
        v.pb(dfs2(G[x][i]));
    }
  if(x==p[mem])v.pb(s);
    sort(v.begin(),v.end());
    
    if(v.size()==0){
        return num[x]=0;
    }
    int a=-1;
    rep(i,v.size()){
        if(v[i]==a+1){a++;continue;}
        if(v[i]==a){continue;}
        break;
    }
    a++;
    return num[x]=a;
}
int main(){
    int n;cin>>n;
    rep2(i,1,n){
        cin>>p[i];
        G[p[i]].pb(i);
    }
    int temp=1;
    visited[1]=1;
    while(1){
        if(visited[p[temp]])break;
        visited[p[temp]]=1;
        temp=p[temp];
    }
    mem=temp;
    if(dfs(temp)!=num[p[temp]]) {cout<<"POSSIBLE";return 0;}
    s=num[p[temp]];
    if(s==dfs2(temp)){cout<<"POSSIBLE";}
    else cout<<"IMPOSSIBLE";
    
}



### Prompt

Create a solution in cpp for 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 rep2(i,a,b) for(int i=a;i<=b;++i)
#define rep(i,n) for(int i=0;i<n;i++)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define tii tuple<int,int,int>
#define pq priority_queue<int>
#define pqg priority_queue<int,vector<int>,greater<int>>
#define pb push_back
#define edge(v,a,b) v[a].pb(b);v[b].pb(a);
ll MOD=998244353;
#define INF 2*1e9
#define N 600010
#define MAX_V 900010
using namespace std;
int visited[N],num[N];
int mem,p[N],s;
vector<int> G[N];
int dfs(int x){
    vector<int> v;
    rep(i,G[x].size()){
        if(G[x][i]==mem)continue;
        v.pb(dfs(G[x][i]));
    }
    sort(v.begin(),v.end());
    if(v.size()==0){
        return num[x]=0;
    }
    int a=-1;
    rep(i,v.size()){
        if(v[i]==a+1){a++;continue;}
        if(v[i]==a){continue;}
        break;
    }
    a++;
    return num[x]=a;
}
int dfs2(int x){
    vector<int> v;
    rep(i,G[x].size()){
        if(G[x][i]==mem)continue;
        v.pb(dfs2(G[x][i]));
    }
  if(x==p[mem])v.pb(s);
    sort(v.begin(),v.end());
    
    if(v.size()==0){
        return num[x]=0;
    }
    int a=-1;
    rep(i,v.size()){
        if(v[i]==a+1){a++;continue;}
        if(v[i]==a){continue;}
        break;
    }
    a++;
    return num[x]=a;
}
int main(){
    int n;cin>>n;
    rep2(i,1,n){
        cin>>p[i];
        G[p[i]].pb(i);
    }
    int temp=1;
    visited[1]=1;
    while(1){
        if(visited[p[temp]])break;
        visited[p[temp]]=1;
        temp=p[temp];
    }
    mem=temp;
    if(dfs(temp)!=num[p[temp]]) {cout<<"POSSIBLE";return 0;}
    s=num[p[temp]];
    if(s==dfs2(temp)){cout<<"POSSIBLE";}
    else cout<<"IMPOSSIBLE";
    
}



```