#include<bits/stdc++.h>
#define ll long long
using namespace std;
int n,tot,mx,mn,e[500010],hd[500010],nt[500010],f[500010],v[500010],mp[500010],cnt,fa[500010];
void build(int x,int y){
	tot++;
	e[tot]=y;
	nt[tot]=hd[x];hd[x]=tot;
}
void dfs(int x){
	int i;
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		dfs(e[i]);
	}
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		v[f[e[i]]]=1;
	}
	while(v[f[x]])f[x]++;
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		v[f[e[i]]]=0;
	}
}
int main(){
	int i,x;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&fa[i]);
		build(fa[i],i);
	}
	x=1;
	while(!v[x])v[x]=1,x=fa[x];
	while(!mp[x])mp[x]=1,x=fa[x];
	for(i=0;i<=n;i++)v[i]=0;
	mn=n+1;
	for(i=1;i<=n;i++)if(mp[i]){
		dfs(i);
		mx=max(mx,f[i]);
		mn=min(mn,f[i]);cnt++;
	}
	if(mx==mn&&cnt%2==1)puts("IMPOSSIBLE");
	 else puts("POSSIBLE");
}
### Prompt

In CPP, your task is to solve 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>
#define ll long long
using namespace std;
int n,tot,mx,mn,e[500010],hd[500010],nt[500010],f[500010],v[500010],mp[500010],cnt,fa[500010];
void build(int x,int y){
	tot++;
	e[tot]=y;
	nt[tot]=hd[x];hd[x]=tot;
}
void dfs(int x){
	int i;
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		dfs(e[i]);
	}
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		v[f[e[i]]]=1;
	}
	while(v[f[x]])f[x]++;
	for(i=hd[x];i;i=nt[i]){
		if(mp[e[i]])continue;
		v[f[e[i]]]=0;
	}
}
int main(){
	int i,x;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&fa[i]);
		build(fa[i],i);
	}
	x=1;
	while(!v[x])v[x]=1,x=fa[x];
	while(!mp[x])mp[x]=1,x=fa[x];
	for(i=0;i<=n;i++)v[i]=0;
	mn=n+1;
	for(i=1;i<=n;i++)if(mp[i]){
		dfs(i);
		mx=max(mx,f[i]);
		mn=min(mn,f[i]);cnt++;
	}
	if(mx==mn&&cnt%2==1)puts("IMPOSSIBLE");
	 else puts("POSSIBLE");
}
```