#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <vector>
#define N 200011
using namespace std;
int ti,All[N],siz,tot,indexx[N],dp[N],vist[N],hashh[N],n,fa[N],cir[N],cnt;
vector<int> V[N];
struct apple{
	int v,nxt;
}edge[N*4];
void addedge(int x,int y){
	edge[++tot].v=y;
	edge[tot].nxt=indexx[x];
	indexx[x]=tot;
}
void dfs(int u,int f){
	int t=indexx[u],vv;
	while(t){
		vv=edge[t].v;
		if(!cir[vv] || vv==f){
			dfs(vv,u);
			V[u].push_back(dp[vv]);
		}
		t=edge[t].nxt;
	}
	ti++;
	int len=V[u].size();
	for(int i=0;i<len;i++){
		hashh[V[u][i]]=ti;
	}
	for(int i=0;i<=n*2;i++){
		if(hashh[i]!=ti){
			dp[u]=i;
			break;
		}
	}
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&fa[i]);
		addedge(fa[i],i);
	}
	int x=1;
	while(1){
		if(vist[x]) break;
		vist[x]=1;
		x=fa[x];
	}
	memset(vist,0,sizeof(vist));
	int u=x;
	while(1){
		if(cir[u]) break;
		cir[u]=1;
		cnt++;
		u=fa[u];
	}
	if(cnt%2==0){
		printf("POSSIBLE");
		return 0;
	}
	u=x;
	while(1){
		if(vist[u]) break;
		vist[u]=1;
		dfs(u,0);
		All[++siz]=dp[u];
		u=fa[u];
	}
	sort(All+1,All+siz+1);
	for(int i=1;i<siz;i++){
		if(All[i]!=All[i+1]){
			printf("POSSIBLE");
			return 0;
		}
	}
	printf("IMPOSSIBLE");
	return 0;
}
### Prompt

Please formulate 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 <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <vector>
#define N 200011
using namespace std;
int ti,All[N],siz,tot,indexx[N],dp[N],vist[N],hashh[N],n,fa[N],cir[N],cnt;
vector<int> V[N];
struct apple{
	int v,nxt;
}edge[N*4];
void addedge(int x,int y){
	edge[++tot].v=y;
	edge[tot].nxt=indexx[x];
	indexx[x]=tot;
}
void dfs(int u,int f){
	int t=indexx[u],vv;
	while(t){
		vv=edge[t].v;
		if(!cir[vv] || vv==f){
			dfs(vv,u);
			V[u].push_back(dp[vv]);
		}
		t=edge[t].nxt;
	}
	ti++;
	int len=V[u].size();
	for(int i=0;i<len;i++){
		hashh[V[u][i]]=ti;
	}
	for(int i=0;i<=n*2;i++){
		if(hashh[i]!=ti){
			dp[u]=i;
			break;
		}
	}
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&fa[i]);
		addedge(fa[i],i);
	}
	int x=1;
	while(1){
		if(vist[x]) break;
		vist[x]=1;
		x=fa[x];
	}
	memset(vist,0,sizeof(vist));
	int u=x;
	while(1){
		if(cir[u]) break;
		cir[u]=1;
		cnt++;
		u=fa[u];
	}
	if(cnt%2==0){
		printf("POSSIBLE");
		return 0;
	}
	u=x;
	while(1){
		if(vist[u]) break;
		vist[u]=1;
		dfs(u,0);
		All[++siz]=dp[u];
		u=fa[u];
	}
	sort(All+1,All+siz+1);
	for(int i=1;i<siz;i++){
		if(All[i]!=All[i+1]){
			printf("POSSIBLE");
			return 0;
		}
	}
	printf("IMPOSSIBLE");
	return 0;
}
```