#include <cstdio>
#include <cstring>
#define MAXN 200010

struct edge{
	int to,next;
	edge(int _to=0,int _next=0):to(_to),next(_next){}
}e[MAXN];

int n,root;
int g[MAXN],nume;
int p[MAXN];
bool visit[MAXN];
int f[MAXN];
bool cnt[MAXN];

void addEdge(int u,int v){
	e[nume]=edge(v,g[u]);
	g[u]=nume++;
}

void dfs(int x){
	for(int i=g[x];~i;i=e[i].next)
		if(e[i].to!=root) 
			dfs(e[i].to);
	for(int i=g[x];~i;i=e[i].next) 
		if(f[e[i].to]>=0) 
			cnt[f[e[i].to]]=1;
	for(f[x]=0;cnt[f[x]];f[x]++);
	for(int i=g[x];~i;i=e[i].next) 
		if(f[e[i].to]>=0) 
			cnt[f[e[i].to]]=0;
}

bool check(){
	int x=p[root];
	for(int i=g[x];~i;i=e[i].next)
		cnt[f[e[i].to]]=1;
	bool flag=1;
	if(cnt[f[x]]) flag=0;
	for(int i=0;i<f[x];i++) if(!cnt[i]) flag=0;
	memset(cnt,0,sizeof cnt);
	return flag;
}

bool gao(){
	int x=1;
	while(!visit[x]) visit[x]=1,x=p[x];
	memset(visit,0,sizeof visit);
	memset(f,-1,sizeof f);
	root=x;
	dfs(root);
	if(check()) return 1;
	int f0=f[p[x]];
	memset(f,-1,sizeof f);
	f[root]=f0;
	dfs(root);
	if(check()) return 1;
	return 0;
}

int main(){
	memset(g,-1,sizeof g);
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",p+i),addEdge(p[i],i);
	if(gao()) puts("POSSIBLE");
	else puts("IMPOSSIBLE");
}
### 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 <cstdio>
#include <cstring>
#define MAXN 200010

struct edge{
	int to,next;
	edge(int _to=0,int _next=0):to(_to),next(_next){}
}e[MAXN];

int n,root;
int g[MAXN],nume;
int p[MAXN];
bool visit[MAXN];
int f[MAXN];
bool cnt[MAXN];

void addEdge(int u,int v){
	e[nume]=edge(v,g[u]);
	g[u]=nume++;
}

void dfs(int x){
	for(int i=g[x];~i;i=e[i].next)
		if(e[i].to!=root) 
			dfs(e[i].to);
	for(int i=g[x];~i;i=e[i].next) 
		if(f[e[i].to]>=0) 
			cnt[f[e[i].to]]=1;
	for(f[x]=0;cnt[f[x]];f[x]++);
	for(int i=g[x];~i;i=e[i].next) 
		if(f[e[i].to]>=0) 
			cnt[f[e[i].to]]=0;
}

bool check(){
	int x=p[root];
	for(int i=g[x];~i;i=e[i].next)
		cnt[f[e[i].to]]=1;
	bool flag=1;
	if(cnt[f[x]]) flag=0;
	for(int i=0;i<f[x];i++) if(!cnt[i]) flag=0;
	memset(cnt,0,sizeof cnt);
	return flag;
}

bool gao(){
	int x=1;
	while(!visit[x]) visit[x]=1,x=p[x];
	memset(visit,0,sizeof visit);
	memset(f,-1,sizeof f);
	root=x;
	dfs(root);
	if(check()) return 1;
	int f0=f[p[x]];
	memset(f,-1,sizeof f);
	f[root]=f0;
	dfs(root);
	if(check()) return 1;
	return 0;
}

int main(){
	memset(g,-1,sizeof g);
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",p+i),addEdge(p[i],i);
	if(gao()) puts("POSSIBLE");
	else puts("IMPOSSIBLE");
}
```