#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <algorithm>
using namespace std;

int n,i,j,k,l,r,u,v,pre,val;
int tmp[200005],T;
int q[200005],p[200005],init[200005];
int col[200005];
vector<int> V[200005];

void fail(){printf("IMPOSSIBLE\n");exit(0);}

int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d",&p[i]),++init[p[i]];
	for(i=1;i<=n;++i)if(!init[i])q[++r]=i;
	for(l=1;l<=r;++l)
	{
		u=q[l];
		++T;
		for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
		for(i=0;tmp[i]==T;++i);
		col[u]=i;
		V[p[u]].push_back(i);
		if(!(--init[p[u]]))q[++r]=p[u];
	}
	
	for(i=1;i<=n;++i)if(init[i]){u=i;break;}
	
	++T;
	for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
	for(k=0;tmp[k]==T;++k);
	pre=val=k;
	for(i=p[u];i!=u;i=p[i])
	{
		++T;
		tmp[pre]=T;
		for(j=0;j<V[i].size();++j)tmp[V[i][j]]=T;
		for(j=0;tmp[j]==T;++j);
		pre=j;
	}
	if(pre!=val)
	{
		printf("POSSIBLE\n");
		return 0;
	}
	
	++T;
	for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
	for(k=0;tmp[k]==T;++k);
	val=k;
	for(++k;tmp[k]==T;++k);
	pre=k;
	for(i=p[u];i!=u;i=p[i])
	{
		++T;
		tmp[pre]=T;
		for(j=0;j<V[i].size();++j)tmp[V[i][j]]=T;
		for(j=0;tmp[j]==T;++j);
		pre=j;
	}
	if(pre==val)printf("POSSIBLE\n");
	else printf("IMPOSSIBLE\n");
}
### 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 <stdio.h>
#include <stdlib.h>
#include <vector>
#include <algorithm>
using namespace std;

int n,i,j,k,l,r,u,v,pre,val;
int tmp[200005],T;
int q[200005],p[200005],init[200005];
int col[200005];
vector<int> V[200005];

void fail(){printf("IMPOSSIBLE\n");exit(0);}

int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d",&p[i]),++init[p[i]];
	for(i=1;i<=n;++i)if(!init[i])q[++r]=i;
	for(l=1;l<=r;++l)
	{
		u=q[l];
		++T;
		for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
		for(i=0;tmp[i]==T;++i);
		col[u]=i;
		V[p[u]].push_back(i);
		if(!(--init[p[u]]))q[++r]=p[u];
	}
	
	for(i=1;i<=n;++i)if(init[i]){u=i;break;}
	
	++T;
	for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
	for(k=0;tmp[k]==T;++k);
	pre=val=k;
	for(i=p[u];i!=u;i=p[i])
	{
		++T;
		tmp[pre]=T;
		for(j=0;j<V[i].size();++j)tmp[V[i][j]]=T;
		for(j=0;tmp[j]==T;++j);
		pre=j;
	}
	if(pre!=val)
	{
		printf("POSSIBLE\n");
		return 0;
	}
	
	++T;
	for(i=0;i<V[u].size();++i)tmp[V[u][i]]=T;
	for(k=0;tmp[k]==T;++k);
	val=k;
	for(++k;tmp[k]==T;++k);
	pre=k;
	for(i=p[u];i!=u;i=p[i])
	{
		++T;
		tmp[pre]=T;
		for(j=0;j<V[i].size();++j)tmp[V[i][j]]=T;
		for(j=0;tmp[j]==T;++j);
		pre=j;
	}
	if(pre==val)printf("POSSIBLE\n");
	else printf("IMPOSSIBLE\n");
}
```