#include<bits/stdc++.h>
using namespace std;
#define N 200010
 
int n,t,p[N],h[N],a[N];
vector<int> q,v[N],f;
 
void travel(int x){
	for (int i=0;i<(int)v[x].size();i++)
		if (!h[v[x][i]]) travel(v[x][i]);
	f.clear();
	for (int i=0;i<(int)v[x].size();i++)
		if (!h[v[x][i]]) f.push_back(a[v[x][i]]);
	f.push_back(-1);f.push_back(1e9);a[x]=-1;
	sort(f.begin(),f.end());
	for (int i=0;a[x]==f[i];)
		for (a[x]++;a[x]==f[i+1];) i++;
}

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&p[i]);
	for (int i=1;i<=n;i++) v[p[i]].push_back(i);
	for (int i=t=1;i<=n;i++) t=p[t];
	for (;!h[t];t=p[t]) h[t]=1,q.push_back(t);
	for (int i=0;i<(int)q.size();i++) travel(q[i]);
	for (int i=1;i<(int)q.size();i++)
		if (a[q[i]]!=a[q[i-1]]) {printf("POSSIBLE\n");return 0;}
	printf(q.size()%2?"IMPOSSIBLE\n":"POSSIBLE\n");
	return 0;
}
### Prompt

Create a solution in CPP for 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<bits/stdc++.h>
using namespace std;
#define N 200010
 
int n,t,p[N],h[N],a[N];
vector<int> q,v[N],f;
 
void travel(int x){
	for (int i=0;i<(int)v[x].size();i++)
		if (!h[v[x][i]]) travel(v[x][i]);
	f.clear();
	for (int i=0;i<(int)v[x].size();i++)
		if (!h[v[x][i]]) f.push_back(a[v[x][i]]);
	f.push_back(-1);f.push_back(1e9);a[x]=-1;
	sort(f.begin(),f.end());
	for (int i=0;a[x]==f[i];)
		for (a[x]++;a[x]==f[i+1];) i++;
}

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&p[i]);
	for (int i=1;i<=n;i++) v[p[i]].push_back(i);
	for (int i=t=1;i<=n;i++) t=p[t];
	for (;!h[t];t=p[t]) h[t]=1,q.push_back(t);
	for (int i=0;i<(int)q.size();i++) travel(q[i]);
	for (int i=1;i<(int)q.size();i++)
		if (a[q[i]]!=a[q[i-1]]) {printf("POSSIBLE\n");return 0;}
	printf(q.size()%2?"IMPOSSIBLE\n":"POSSIBLE\n");
	return 0;
}
```