#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define int long long
using namespace std;
struct edge {
	int u,v,nxt;
} e[233333*2];
int n,tot,h[233333],p[233333],incir[233333],cir[233333],f[233333],vis[233333];
void add(int u,int v) {
	e[++tot].u=u;
	e[tot].v=v;
	e[tot].nxt=h[u];
	h[u]=tot;
}
void dfs_sub_tree(int u){
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v]) continue;
		dfs_sub_tree(v);
	}
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v])continue;
		vis[f[v]]=1;
	}
	while(vis[f[u]])f[u]++;
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v])continue;
		vis[f[v]]=0;
	}
}
signed main() {
	scanf("%lld",&n);
	for(int i=1; i<=n; ++i) {
		scanf("%lld",&p[i]);
		add(p[i],i);
	}
	int now=1;
	while(!incir[now]) {
		incir[now]=1;
		now=p[now];
	}
	memset(incir,0,sizeof(incir));
	while(!incir[now]) {
		incir[now]=1;
		cir[++cir[0]]=now;
		now=p[now];
	}
	if(cir[0]%2==0){
		cout<<"POSSIBLE";
		return 0;
	}
	int maxn=0,minm=n*2;
	for(int i=1;i<=cir[0];++i){
		dfs_sub_tree(cir[i]);
		maxn=max(maxn,f[cir[i]]);
		minm=min(minm,f[cir[i]]);
	}
	if(maxn!=minm){
		cout<<"POSSIBLE";
	}
	else cout<<"IMPOSSIBLE";
}
### Prompt

Generate 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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define int long long
using namespace std;
struct edge {
	int u,v,nxt;
} e[233333*2];
int n,tot,h[233333],p[233333],incir[233333],cir[233333],f[233333],vis[233333];
void add(int u,int v) {
	e[++tot].u=u;
	e[tot].v=v;
	e[tot].nxt=h[u];
	h[u]=tot;
}
void dfs_sub_tree(int u){
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v]) continue;
		dfs_sub_tree(v);
	}
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v])continue;
		vis[f[v]]=1;
	}
	while(vis[f[u]])f[u]++;
	for(int i=h[u];i;i=e[i].nxt){
		int v=e[i].v;
		if(incir[v])continue;
		vis[f[v]]=0;
	}
}
signed main() {
	scanf("%lld",&n);
	for(int i=1; i<=n; ++i) {
		scanf("%lld",&p[i]);
		add(p[i],i);
	}
	int now=1;
	while(!incir[now]) {
		incir[now]=1;
		now=p[now];
	}
	memset(incir,0,sizeof(incir));
	while(!incir[now]) {
		incir[now]=1;
		cir[++cir[0]]=now;
		now=p[now];
	}
	if(cir[0]%2==0){
		cout<<"POSSIBLE";
		return 0;
	}
	int maxn=0,minm=n*2;
	for(int i=1;i<=cir[0];++i){
		dfs_sub_tree(cir[i]);
		maxn=max(maxn,f[cir[i]]);
		minm=min(minm,f[cir[i]]);
	}
	if(maxn!=minm){
		cout<<"POSSIBLE";
	}
	else cout<<"IMPOSSIBLE";
}
```