#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
int outgo[202020];
int du[202020];
int a[202020];
struct Edge
{
	int val,next;
}edges[202020];
int first[202020];
int te=1;
int cnt;
int visit[202020];
inline int get(int now)
{
	cnt++;
	for(int e=first[now];e;e=edges[e].next)
		visit[edges[e].val]=cnt;
	int i;
	for(i=0;visit[i]==cnt;i++);
	return i;
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&outgo[i]);
		du[outgo[i]]++;
	}
	queue<int> q;
	for(int i=1;i<=n;i++)
		if(!du[i])
			q.push(i);
	int visitcnt=0;
	while(!q.empty())
	{
		int now=q.front();
		q.pop();
		visitcnt++;
		int to=outgo[now];
		a[now]=get(now);
		te++;
		edges[te].val=a[now];
		edges[te].next=first[to];
		first[to]=te;
		if(!(--du[to]))
			q.push(to);
	}
	if((n-visitcnt)%2==0)
	{
		puts("POSSIBLE");
		return 0;
	}
	int k=-1;
	for(int i=1;i<=n;i++)
		if(du[i])
		{
			int tmp=get(i);
			if(k==-1)
				k=tmp;
			if(k!=tmp)
			{
				puts("POSSIBLE");
				return 0;
			}
		}
	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<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
int outgo[202020];
int du[202020];
int a[202020];
struct Edge
{
	int val,next;
}edges[202020];
int first[202020];
int te=1;
int cnt;
int visit[202020];
inline int get(int now)
{
	cnt++;
	for(int e=first[now];e;e=edges[e].next)
		visit[edges[e].val]=cnt;
	int i;
	for(i=0;visit[i]==cnt;i++);
	return i;
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&outgo[i]);
		du[outgo[i]]++;
	}
	queue<int> q;
	for(int i=1;i<=n;i++)
		if(!du[i])
			q.push(i);
	int visitcnt=0;
	while(!q.empty())
	{
		int now=q.front();
		q.pop();
		visitcnt++;
		int to=outgo[now];
		a[now]=get(now);
		te++;
		edges[te].val=a[now];
		edges[te].next=first[to];
		first[to]=te;
		if(!(--du[to]))
			q.push(to);
	}
	if((n-visitcnt)%2==0)
	{
		puts("POSSIBLE");
		return 0;
	}
	int k=-1;
	for(int i=1;i<=n;i++)
		if(du[i])
		{
			int tmp=get(i);
			if(k==-1)
				k=tmp;
			if(k!=tmp)
			{
				puts("POSSIBLE");
				return 0;
			}
		}
	puts("IMPOSSIBLE");
	return 0;
}
```