#include<bits/stdc++.h>
#define L long long
#define pb push_back
#define pi pair<int,int>
#define pii pair<pair<int,int>,int>
#define aa first
#define bb second
#define xx aa.aa
#define yy aa.bb
#define zz bb
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
int n,f[200010],x[200010],b[200010],c[200010],w[200010],p;
vector<int> a[200010];
inline void get(int i)
{
	int j;
	for(auto j:a[i])
	  w[f[j]]++;
	for(j=0;w[j];j++);
	f[i]=j;
	for(auto j:a[i])
	  w[f[j]]--;
}
inline void get2(int i)
{
	int j;
	for(auto j:a[i])
	  w[f[j]]++;
	for(j=0;w[j];j++);
	for(j++;w[j];j++);
	f[i]=j;
	for(auto j:a[i])
	  w[f[j]]--;
}
inline void dfs(int i)
{
	for(auto j:a[i])
	  dfs(j);
	get(i);
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  {
	   scanf("%d",&x[i]);
	   a[x[i]].pb(i);
	  }
	for(i=1;b[i]<2;i=x[i])
	  {
	   b[i]++;
	   if(b[i]==2)
	     c[++p]=i;
	  }
	for(i=1;i<=p;i++)
	  for(auto j:a[c[i]])
	    if(b[j]<2)
	      dfs(j);
	f[c[p]]=n+5;
	get(c[1]);
	for(i=2;i<=p;i++)
	  get(c[i]);
	i=f[c[1]];
	get(c[1]);
	if(i==f[c[1]])
	  {
	   printf("POSSIBLE\n");
	   return 0;
	  }
	f[c[p]]=n+5;
	get2(c[1]);
	for(i=2;i<=p;i++)
	  get(c[i]);
	i=f[c[1]];
	get(c[1]);
	if(i==f[c[1]])
	  printf("POSSIBLE\n");
	else
	  printf("IMPOSSIBLE\n");
	return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 L long long
#define pb push_back
#define pi pair<int,int>
#define pii pair<pair<int,int>,int>
#define aa first
#define bb second
#define xx aa.aa
#define yy aa.bb
#define zz bb
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
int n,f[200010],x[200010],b[200010],c[200010],w[200010],p;
vector<int> a[200010];
inline void get(int i)
{
	int j;
	for(auto j:a[i])
	  w[f[j]]++;
	for(j=0;w[j];j++);
	f[i]=j;
	for(auto j:a[i])
	  w[f[j]]--;
}
inline void get2(int i)
{
	int j;
	for(auto j:a[i])
	  w[f[j]]++;
	for(j=0;w[j];j++);
	for(j++;w[j];j++);
	f[i]=j;
	for(auto j:a[i])
	  w[f[j]]--;
}
inline void dfs(int i)
{
	for(auto j:a[i])
	  dfs(j);
	get(i);
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  {
	   scanf("%d",&x[i]);
	   a[x[i]].pb(i);
	  }
	for(i=1;b[i]<2;i=x[i])
	  {
	   b[i]++;
	   if(b[i]==2)
	     c[++p]=i;
	  }
	for(i=1;i<=p;i++)
	  for(auto j:a[c[i]])
	    if(b[j]<2)
	      dfs(j);
	f[c[p]]=n+5;
	get(c[1]);
	for(i=2;i<=p;i++)
	  get(c[i]);
	i=f[c[1]];
	get(c[1]);
	if(i==f[c[1]])
	  {
	   printf("POSSIBLE\n");
	   return 0;
	  }
	f[c[p]]=n+5;
	get2(c[1]);
	for(i=2;i<=p;i++)
	  get(c[i]);
	i=f[c[1]];
	get(c[1]);
	if(i==f[c[1]])
	  printf("POSSIBLE\n");
	else
	  printf("IMPOSSIBLE\n");
	return 0;
}

```