#include<bits/stdc++.h>
using namespace std;
int n,tot;
vector<int>ed[200001];
vector<int>e[200001];
int topo[200001];
int in[200001];
int sg[200001];
void toposort()
{
	queue<int> q;
	for(int i=1;i<=n;i++)
		in[i]=0;
	for(int u=1;u<=n;u++)
	{
		for(int i=0;i<ed[u].size();i++)
		{
			int to=ed[u][i];
			in[to]++;
		}
	}
	for(int i=1;i<=n;i++)
		if(in[i]==0)
			q.push(i);
	while(!q.empty())
	{
		int u=q.front();
		q.pop();
		topo[++tot]=u;
		for(int i=0;i<ed[u].size();i++)
		{
			int to=ed[u][i];
			in[to]--;
			if(in[to]==0)
				q.push(to);
		}
	}
}
signed main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int x;
		scanf("%d",&x);
		ed[i].push_back(x);
		e[x].push_back(i);
	}
	toposort();
	for(int i=1;i<=n;i++)
		if(in[i]!=0)
			topo[++tot]=i;
	for(int j=1;j<=n;j++)
	{
		int u=topo[j];
		map<int,int> mp;
		for(int i=0;i<e[u].size();i++)
		{
			int to=e[u][i];
			if(in[to]==0) mp[sg[to]]=1;
		}
		while(mp[sg[u]]==1)++sg[u];
	}
	int num=-1,cnt=0;
	for(int i=1;i<=n;i++)
		if(in[i]!=0)
		{
			if(num==-1) num=sg[i];
			if(num!=sg[i])
			{
				printf("POSSIBLE");
				return 0;
			}
			cnt++;
		}
	if(num==-1||cnt%2==0)printf("POSSIBLE");
	else printf("IMPOSSIBLE");
	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>
using namespace std;
int n,tot;
vector<int>ed[200001];
vector<int>e[200001];
int topo[200001];
int in[200001];
int sg[200001];
void toposort()
{
	queue<int> q;
	for(int i=1;i<=n;i++)
		in[i]=0;
	for(int u=1;u<=n;u++)
	{
		for(int i=0;i<ed[u].size();i++)
		{
			int to=ed[u][i];
			in[to]++;
		}
	}
	for(int i=1;i<=n;i++)
		if(in[i]==0)
			q.push(i);
	while(!q.empty())
	{
		int u=q.front();
		q.pop();
		topo[++tot]=u;
		for(int i=0;i<ed[u].size();i++)
		{
			int to=ed[u][i];
			in[to]--;
			if(in[to]==0)
				q.push(to);
		}
	}
}
signed main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int x;
		scanf("%d",&x);
		ed[i].push_back(x);
		e[x].push_back(i);
	}
	toposort();
	for(int i=1;i<=n;i++)
		if(in[i]!=0)
			topo[++tot]=i;
	for(int j=1;j<=n;j++)
	{
		int u=topo[j];
		map<int,int> mp;
		for(int i=0;i<e[u].size();i++)
		{
			int to=e[u][i];
			if(in[to]==0) mp[sg[to]]=1;
		}
		while(mp[sg[u]]==1)++sg[u];
	}
	int num=-1,cnt=0;
	for(int i=1;i<=n;i++)
		if(in[i]!=0)
		{
			if(num==-1) num=sg[i];
			if(num!=sg[i])
			{
				printf("POSSIBLE");
				return 0;
			}
			cnt++;
		}
	if(num==-1||cnt%2==0)printf("POSSIBLE");
	else printf("IMPOSSIBLE");
	return 0;
}

```