#include <bits/stdc++.h>
#define int long long
#define mp make_pair
#define pb push_back
#define ld long double
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define piii pair<pii,pii>
#define precise cout<<fixed<<setprecision(10)
#define st first
#define nd second
#define ins insert
#define vi vector<int>
#define BOOST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
const int MAX=2e5+5;
vi P[MAX];
int a[MAX],grundy[MAX],p[MAX],root,forb,n;
bool O[MAX];
int Find(int u){
	if (p[u]!=u)p[u]=Find(p[u]);
	return p[u];
}

void Union(int u,int v){
	p[Find(u)]=Find(v);
}

void dfs(int u){
	if (u==forb)return;
	if (!sz(P[u]))return;
	for (auto it:P[u])dfs(it);
	for (auto it:P[u])O[grundy[it]]=true;
	for (int i=0;i<=n+2;i++) if (!O[i]){grundy[u]=i;break;}
	for (auto it:P[u])O[grundy[it]]=false;
}

int32_t main()
{
  BOOST;
  cin>>n;
  iota(p+1,p+n+1,1);
  for (int i=1;i<=n;i++){
  	cin>>a[i];
  	if (Find(a[i])==Find(i))root=i;
  	else Union(a[i],i),P[a[i]].pb(i);
  }
  dfs(root);
  if (grundy[root]==grundy[a[root]]){
  	forb=a[root];
  	grundy[a[root]]++;
  	dfs(root);
  	if (grundy[root]!=grundy[a[root]]-1)cout<<"IM";
  }
  cout<<"POSSIBLE";
  return 0;
}

### Prompt

In CPP, your task is to solve 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 int long long
#define mp make_pair
#define pb push_back
#define ld long double
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define piii pair<pii,pii>
#define precise cout<<fixed<<setprecision(10)
#define st first
#define nd second
#define ins insert
#define vi vector<int>
#define BOOST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
const int MAX=2e5+5;
vi P[MAX];
int a[MAX],grundy[MAX],p[MAX],root,forb,n;
bool O[MAX];
int Find(int u){
	if (p[u]!=u)p[u]=Find(p[u]);
	return p[u];
}

void Union(int u,int v){
	p[Find(u)]=Find(v);
}

void dfs(int u){
	if (u==forb)return;
	if (!sz(P[u]))return;
	for (auto it:P[u])dfs(it);
	for (auto it:P[u])O[grundy[it]]=true;
	for (int i=0;i<=n+2;i++) if (!O[i]){grundy[u]=i;break;}
	for (auto it:P[u])O[grundy[it]]=false;
}

int32_t main()
{
  BOOST;
  cin>>n;
  iota(p+1,p+n+1,1);
  for (int i=1;i<=n;i++){
  	cin>>a[i];
  	if (Find(a[i])==Find(i))root=i;
  	else Union(a[i],i),P[a[i]].pb(i);
  }
  dfs(root);
  if (grundy[root]==grundy[a[root]]){
  	forb=a[root];
  	grundy[a[root]]++;
  	dfs(root);
  	if (grundy[root]!=grundy[a[root]]-1)cout<<"IM";
  }
  cout<<"POSSIBLE";
  return 0;
}

```