#include<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
#define pb push_back

int gi() {
	int x=0,o=1;char ch=getchar();
	while(!isdigit(ch)&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n,p[N],sg[N],x;
vector<int> E[N];
bool vis[N],vv[N];

int dfs(int u) {
	if(vis[u]) return u;
	vis[u]=1;
	return dfs(p[u]);
}

void dfs2(int u) {
	for(auto v:E[u])
		if(!vis[v]) dfs2(v);
	for(auto v:E[u])
		if(!vis[v]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]) { sg[u]=i;break; }
	for(auto v:E[u]) vv[sg[v]]=0;

}

void solve(int u) {
	if(u==x) {
		for(auto v:E[u]) vv[sg[v]]=1;
		for(int i=0;;i++)
			if(!vv[i]) {
				if(sg[u]==i) { cout<<"POSSIBLE";exit(0); }
				else break;
			}
		for(auto v:E[u]) vv[sg[v]]=0;
		return;
	}
	for(auto v:E[u]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]) { sg[u]=i;break; }
	for(auto v:E[u]) vv[sg[v]]=0;
	solve(p[u]);
}

int main() {
	cin>>n;
	for(int i=1;i<=n;i++) E[p[i]=gi()].pb(i);
	x=dfs(1);int v=x;
	memset(vis,0,sizeof(vis));
	do vis[v]=1,v=p[v]; while(v!=x);
	for(int i=1;i<=n;i++)
		if(vis[i]) dfs2(i);
	solve(p[x]);
	for(auto v:E[x]) if(!vis[v]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]&&sg[x]!=i) { sg[x]=i;break; }
	for(auto v:E[x]) vv[sg[v]]=0;
	solve(p[x]);
	cout<<"IMPOSSIBLE";
	return 0;
}

### Prompt

Your challenge is to write 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<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
#define pb push_back

int gi() {
	int x=0,o=1;char ch=getchar();
	while(!isdigit(ch)&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n,p[N],sg[N],x;
vector<int> E[N];
bool vis[N],vv[N];

int dfs(int u) {
	if(vis[u]) return u;
	vis[u]=1;
	return dfs(p[u]);
}

void dfs2(int u) {
	for(auto v:E[u])
		if(!vis[v]) dfs2(v);
	for(auto v:E[u])
		if(!vis[v]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]) { sg[u]=i;break; }
	for(auto v:E[u]) vv[sg[v]]=0;

}

void solve(int u) {
	if(u==x) {
		for(auto v:E[u]) vv[sg[v]]=1;
		for(int i=0;;i++)
			if(!vv[i]) {
				if(sg[u]==i) { cout<<"POSSIBLE";exit(0); }
				else break;
			}
		for(auto v:E[u]) vv[sg[v]]=0;
		return;
	}
	for(auto v:E[u]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]) { sg[u]=i;break; }
	for(auto v:E[u]) vv[sg[v]]=0;
	solve(p[u]);
}

int main() {
	cin>>n;
	for(int i=1;i<=n;i++) E[p[i]=gi()].pb(i);
	x=dfs(1);int v=x;
	memset(vis,0,sizeof(vis));
	do vis[v]=1,v=p[v]; while(v!=x);
	for(int i=1;i<=n;i++)
		if(vis[i]) dfs2(i);
	solve(p[x]);
	for(auto v:E[x]) if(!vis[v]) vv[sg[v]]=1;
	for(int i=0;;i++)
		if(!vv[i]&&sg[x]!=i) { sg[x]=i;break; }
	for(auto v:E[x]) vv[sg[v]]=0;
	solve(p[x]);
	cout<<"IMPOSSIBLE";
	return 0;
}

```