#include <bits/stdc++.h>
using namespace std;
bool ex[200005];
int deg[200005],a[200005];
vector<int> v[200005],inv[200005];
int main()
{
	int n;
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		int a;
		scanf("%d",&a);
		v[a].push_back(i);
		inv[i].push_back(a);
		deg[a]++;
	}
	set<int> d;
	set<pair<int,int> > s;
	for (int i=1;i<=n;i++)
	s.insert({deg[i],i});
	bool st=0,odd=0;
	memset(a,-1,sizeof(a));
	while (!s.empty())
	{
		auto p=*s.begin();
		s.erase(s.begin());
		if (p.first)
		st=1;
		odd^=st;
		for (int i:v[p.second])
		{
			if (a[i]!=-1)
			ex[a[i]]=1;
		}
		int m=0;
		while (ex[m])
		m++;
		if (st)
		d.insert(m);
		else
		a[p.second]=m;
		for (int i:v[p.second])
		{
			if (a[i]!=-1)
			ex[a[i]]=0;
		}
		for (int i:inv[p.second])
		{
			if (s.find({deg[i],i})!=s.end())
			{
				s.erase({deg[i],i});
				deg[i]--;
				s.insert({deg[i],i});
			}
		}
	}
	if (d.size()==1 && odd)
	printf("IMPOSSIBLE");
	else
	printf("POSSIBLE");
}
### 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>
using namespace std;
bool ex[200005];
int deg[200005],a[200005];
vector<int> v[200005],inv[200005];
int main()
{
	int n;
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		int a;
		scanf("%d",&a);
		v[a].push_back(i);
		inv[i].push_back(a);
		deg[a]++;
	}
	set<int> d;
	set<pair<int,int> > s;
	for (int i=1;i<=n;i++)
	s.insert({deg[i],i});
	bool st=0,odd=0;
	memset(a,-1,sizeof(a));
	while (!s.empty())
	{
		auto p=*s.begin();
		s.erase(s.begin());
		if (p.first)
		st=1;
		odd^=st;
		for (int i:v[p.second])
		{
			if (a[i]!=-1)
			ex[a[i]]=1;
		}
		int m=0;
		while (ex[m])
		m++;
		if (st)
		d.insert(m);
		else
		a[p.second]=m;
		for (int i:v[p.second])
		{
			if (a[i]!=-1)
			ex[a[i]]=0;
		}
		for (int i:inv[p.second])
		{
			if (s.find({deg[i],i})!=s.end())
			{
				s.erase({deg[i],i});
				deg[i]--;
				s.insert({deg[i],i});
			}
		}
	}
	if (d.size()==1 && odd)
	printf("IMPOSSIBLE");
	else
	printf("POSSIBLE");
}
```