#include<bits/stdc++.h>
using namespace std;
#define N 200005
vector<int> v[N];
int fa[N],du[N],sg[N];
int n;
void calc(int u){
	sort(v[u].begin(),v[u].end());
	sg[u]=0;
	for(int i:v[u]) i==sg[u]? sg[u]++:0;
}
void tp(int u){
	calc(u);
	du[fa[u]]--;du[u]=-1;
	v[fa[u]].push_back(sg[u]);
	if(du[fa[u]]==0) tp(fa[u]);
}
vector<int> temp;
void DFS(int u,int top){
	temp.push_back(sg[u]);du[u]=-1; 
	if(fa[u]!=top) DFS(fa[u],top);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&fa[i]),du[fa[i]]++;
	for(int i=1;i<=n;i++)
		if(du[i]==0) tp(i);
	for(int i=1;i<=n;i++)
		if(du[i]==1) calc(i);
	for(int i=1;i<=n;i++)
		if(du[i]==1){
			DFS(i,i);
			sort(temp.begin(),temp.end());
			if(temp[0]==temp[temp.size()-1]&&temp.size()%2==1)
				return puts("IMPOSSIBLE"),0;
			temp.clear();
		}
	return puts("POSSIBLE"),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 200005
vector<int> v[N];
int fa[N],du[N],sg[N];
int n;
void calc(int u){
	sort(v[u].begin(),v[u].end());
	sg[u]=0;
	for(int i:v[u]) i==sg[u]? sg[u]++:0;
}
void tp(int u){
	calc(u);
	du[fa[u]]--;du[u]=-1;
	v[fa[u]].push_back(sg[u]);
	if(du[fa[u]]==0) tp(fa[u]);
}
vector<int> temp;
void DFS(int u,int top){
	temp.push_back(sg[u]);du[u]=-1; 
	if(fa[u]!=top) DFS(fa[u],top);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&fa[i]),du[fa[i]]++;
	for(int i=1;i<=n;i++)
		if(du[i]==0) tp(i);
	for(int i=1;i<=n;i++)
		if(du[i]==1) calc(i);
	for(int i=1;i<=n;i++)
		if(du[i]==1){
			DFS(i,i);
			sort(temp.begin(),temp.end());
			if(temp[0]==temp[temp.size()-1]&&temp.size()%2==1)
				return puts("IMPOSSIBLE"),0;
			temp.clear();
		}
	return puts("POSSIBLE"),0;
}
```