#include<iostream>
#include<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
#include<iomanip>
#include<cstdlib>
#include<cstdio>
#include<map>
#include<bitset>
#include<set>
#include<stack>
#include<vector>
#include<queue>
using namespace std;
#define MAXN 200010
#define MAXM 1010
#define ll long long
#define eps 1e-8
#define MOD 1000000007
#define INF 1000000000
struct vec{
	int to;
	int fro;
};
vec mp[MAXN];
int tai[MAXN],cnt;
int fa[MAXN];
int v[MAXN];
int n;
bool vis[MAXN];
bool ic[MAXN];
int t[MAXN],tot;
int has[MAXN];
int T;
int v2[MAXN];
int sv[MAXN];
inline void be(int x,int y){
	mp[++cnt].to=y;
	mp[cnt].fro=tai[x];
	tai[x]=cnt;
}
void dfs(int x){
	int i,y;
	if(vis[x]){
		return ;
	}
	vis[x]=1;
	for(i=tai[x];i;i=mp[i].fro){
		y=mp[i].to;
		if(!ic[y]){
			dfs(y);
		}
	}
	T++;
	for(i=tai[x];i;i=mp[i].fro){
		y=mp[i].to;
		if(!ic[y]){
			has[v[y]]=T;
		}
	}
	for(;has[v[x]]==T;v[x]++){
		
	}
	v2[x]=v[x]+1;
	for(;has[v2[x]]==T;v2[x]++){
		
	}
}
int main(){
	int i,x;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&x);
		fa[i]=x;
		be(x,i);
	}
	x=1;
	while(!vis[x]){
		vis[x]=1;
		x=fa[x];
	}
	while(!ic[x]){
		ic[x]=1;
		t[++tot]=x;
		x=fa[x];
	}
	memset(vis,0,sizeof(vis));
	for(i=1;i<=n;i++){
		dfs(i);
	}
	sv[t[1]]=v[t[1]];
	for(i=2;i<=tot;i++){
		if(sv[t[i-1]]==v[t[i]]){
			sv[t[i]]=v2[t[i]];
		}else{
			sv[t[i]]=v[t[i]];
		}
	}
	if(sv[t[tot]]!=v[t[1]]){
		printf("POSSIBLE\n");
		return 0;
	}
	sv[t[1]]=v2[t[1]];
	for(i=2;i<=tot;i++){
		if(sv[t[i-1]]==v[t[i]]){
			sv[t[i]]=v2[t[i]];
		}else{
			sv[t[i]]=v[t[i]];
		}
	}
	if(sv[t[tot]]==v[t[1]]){
		printf("POSSIBLE\n");
		return 0;
	}
	printf("IMPOSSIBLE\n");
	return 0;
}

/*

*/

### Prompt

Your task is to create 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<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
#include<iomanip>
#include<cstdlib>
#include<cstdio>
#include<map>
#include<bitset>
#include<set>
#include<stack>
#include<vector>
#include<queue>
using namespace std;
#define MAXN 200010
#define MAXM 1010
#define ll long long
#define eps 1e-8
#define MOD 1000000007
#define INF 1000000000
struct vec{
	int to;
	int fro;
};
vec mp[MAXN];
int tai[MAXN],cnt;
int fa[MAXN];
int v[MAXN];
int n;
bool vis[MAXN];
bool ic[MAXN];
int t[MAXN],tot;
int has[MAXN];
int T;
int v2[MAXN];
int sv[MAXN];
inline void be(int x,int y){
	mp[++cnt].to=y;
	mp[cnt].fro=tai[x];
	tai[x]=cnt;
}
void dfs(int x){
	int i,y;
	if(vis[x]){
		return ;
	}
	vis[x]=1;
	for(i=tai[x];i;i=mp[i].fro){
		y=mp[i].to;
		if(!ic[y]){
			dfs(y);
		}
	}
	T++;
	for(i=tai[x];i;i=mp[i].fro){
		y=mp[i].to;
		if(!ic[y]){
			has[v[y]]=T;
		}
	}
	for(;has[v[x]]==T;v[x]++){
		
	}
	v2[x]=v[x]+1;
	for(;has[v2[x]]==T;v2[x]++){
		
	}
}
int main(){
	int i,x;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&x);
		fa[i]=x;
		be(x,i);
	}
	x=1;
	while(!vis[x]){
		vis[x]=1;
		x=fa[x];
	}
	while(!ic[x]){
		ic[x]=1;
		t[++tot]=x;
		x=fa[x];
	}
	memset(vis,0,sizeof(vis));
	for(i=1;i<=n;i++){
		dfs(i);
	}
	sv[t[1]]=v[t[1]];
	for(i=2;i<=tot;i++){
		if(sv[t[i-1]]==v[t[i]]){
			sv[t[i]]=v2[t[i]];
		}else{
			sv[t[i]]=v[t[i]];
		}
	}
	if(sv[t[tot]]!=v[t[1]]){
		printf("POSSIBLE\n");
		return 0;
	}
	sv[t[1]]=v2[t[1]];
	for(i=2;i<=tot;i++){
		if(sv[t[i-1]]==v[t[i]]){
			sv[t[i]]=v2[t[i]];
		}else{
			sv[t[i]]=v[t[i]];
		}
	}
	if(sv[t[tot]]==v[t[1]]){
		printf("POSSIBLE\n");
		return 0;
	}
	printf("IMPOSSIBLE\n");
	return 0;
}

/*

*/

```