#include<bits/stdc++.h>
#define N 400005
using namespace std;
int n,fa[N],rd[N],fl[N],a[N];
vector<int>s[N];
void OK()
{
	puts("POSSIBLE");
	exit(0);
}
void dfs(int x)
{
	//cout<<x<<endl;
	rd[x]=-1;
	for (int i=0;i<s[x].size();i++)
		fl[a[s[x][i]]]=x;
	for (;fl[a[x]]==x;a[x]++);
	rd[fa[x]]--;
	s[fa[x]].push_back(x);
	if (!rd[fa[x]]) dfs(fa[x]);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&fa[i]);
		rd[fa[i]]++;
	}
	for (int i=1;i<=n;i++)
		if (rd[i]==0) dfs(i);
	//puts("ok");
	for (int i=1;i<=n;i++)
		if (rd[i]>0)
		{
			for (int j=0;j<s[i].size();j++)
				fl[a[s[i][j]]]=i;
			for (;fl[a[i]]==i;a[i]++);
			//cout<<a[i]<<endl;
			int t=fa[i],lst=i;
			while(t!=i)
			{
				for (int j=0;j<s[t].size();j++)
					fl[a[s[t][j]]]=t;
				fl[a[lst]]=t;
				for (;fl[a[t]]==t;a[t]++);
				lst=t;t=fa[t];
			}
			if (a[lst]!=a[i])OK();
			a[i]=a[i]+1;
			t=fa[i],lst=i;
			while(t!=i)
			{
				for (int j=0;j<s[t].size();j++)
					fl[a[s[t][j]]]=t+n;
				fl[a[lst]]=t+n;
				for (a[t]=0;fl[a[t]]==t+n;a[t]++);
				lst=t;t=fa[t];
			}
			if (a[lst]==a[i]-1)OK();
			puts("IMPOSSIBLE");return 0;
		}
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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 N 400005
using namespace std;
int n,fa[N],rd[N],fl[N],a[N];
vector<int>s[N];
void OK()
{
	puts("POSSIBLE");
	exit(0);
}
void dfs(int x)
{
	//cout<<x<<endl;
	rd[x]=-1;
	for (int i=0;i<s[x].size();i++)
		fl[a[s[x][i]]]=x;
	for (;fl[a[x]]==x;a[x]++);
	rd[fa[x]]--;
	s[fa[x]].push_back(x);
	if (!rd[fa[x]]) dfs(fa[x]);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&fa[i]);
		rd[fa[i]]++;
	}
	for (int i=1;i<=n;i++)
		if (rd[i]==0) dfs(i);
	//puts("ok");
	for (int i=1;i<=n;i++)
		if (rd[i]>0)
		{
			for (int j=0;j<s[i].size();j++)
				fl[a[s[i][j]]]=i;
			for (;fl[a[i]]==i;a[i]++);
			//cout<<a[i]<<endl;
			int t=fa[i],lst=i;
			while(t!=i)
			{
				for (int j=0;j<s[t].size();j++)
					fl[a[s[t][j]]]=t;
				fl[a[lst]]=t;
				for (;fl[a[t]]==t;a[t]++);
				lst=t;t=fa[t];
			}
			if (a[lst]!=a[i])OK();
			a[i]=a[i]+1;
			t=fa[i],lst=i;
			while(t!=i)
			{
				for (int j=0;j<s[t].size();j++)
					fl[a[s[t][j]]]=t+n;
				fl[a[lst]]=t+n;
				for (a[t]=0;fl[a[t]]==t+n;a[t]++);
				lst=t;t=fa[t];
			}
			if (a[lst]==a[i]-1)OK();
			puts("IMPOSSIBLE");return 0;
		}
}
```