#include<bits/stdc++.h>
const int N=200007;
int n,fa[N],ed[N],tk=0,deg[N];
std::vector<int>e[N];
int v1[N],v2[N],ss[N],sp=0,ab[N][2];
void f1(int w){
	for(int i=0;i<e[w].size();++i)f1(e[w][i]);
	++tk;
	for(int i=0;i<e[w].size();++i)ed[v1[e[w][i]]]=tk;
	for(v1[w]=0;ed[v1[w]]==tk;++v1[w]);
}
void f2(int w){
	ss[++sp]=w;
	f1(w);
	for(v2[w]=v1[w]+1;ed[v2[w]]==tk;++v2[w]);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",fa+i),++deg[fa[i]];
	std::queue<int>q;
	for(int i=1;i<=n;++i)if(!deg[i])q.push(i);
	while(q.size()){
		int w=q.front(),f=fa[w];q.pop();
		if(!--deg[f])q.push(f);
		e[f].push_back(w);
	}
	for(int i=1;i<=n;++i)if(deg[i]){
		for(int w=i;deg[w];deg[w]=0,f2(w),w=fa[w]);
	}
	ss[0]=ss[sp];
	for(int t=0;t<2;++t){
		ab[0][t]=1,ab[0][t^1]=0;
		for(int i=1;i<=sp;++i){
			int w=ss[i],u=ss[i-1];
			ab[i][0]=ab[i][1]=0;
			for(int j=0;j<2;++j)if(ab[i-1][j]){
				int v=j?v2[u]:v1[u];
				ab[i][v==v1[w]]=1;
			}
		}
		if(ab[sp][t])return puts("POSSIBLE"),0;
	}
	return puts("IMPOSSIBLE"),0;
}
### Prompt

Your challenge is to write a CPP solution to 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>
const int N=200007;
int n,fa[N],ed[N],tk=0,deg[N];
std::vector<int>e[N];
int v1[N],v2[N],ss[N],sp=0,ab[N][2];
void f1(int w){
	for(int i=0;i<e[w].size();++i)f1(e[w][i]);
	++tk;
	for(int i=0;i<e[w].size();++i)ed[v1[e[w][i]]]=tk;
	for(v1[w]=0;ed[v1[w]]==tk;++v1[w]);
}
void f2(int w){
	ss[++sp]=w;
	f1(w);
	for(v2[w]=v1[w]+1;ed[v2[w]]==tk;++v2[w]);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",fa+i),++deg[fa[i]];
	std::queue<int>q;
	for(int i=1;i<=n;++i)if(!deg[i])q.push(i);
	while(q.size()){
		int w=q.front(),f=fa[w];q.pop();
		if(!--deg[f])q.push(f);
		e[f].push_back(w);
	}
	for(int i=1;i<=n;++i)if(deg[i]){
		for(int w=i;deg[w];deg[w]=0,f2(w),w=fa[w]);
	}
	ss[0]=ss[sp];
	for(int t=0;t<2;++t){
		ab[0][t]=1,ab[0][t^1]=0;
		for(int i=1;i<=sp;++i){
			int w=ss[i],u=ss[i-1];
			ab[i][0]=ab[i][1]=0;
			for(int j=0;j<2;++j)if(ab[i-1][j]){
				int v=j?v2[u]:v1[u];
				ab[i][v==v1[w]]=1;
			}
		}
		if(ab[sp][t])return puts("POSSIBLE"),0;
	}
	return puts("IMPOSSIBLE"),0;
}
```