#include<bits/stdc++.h>
#define ll long long
#define mod 998244353
using namespace std;
const int N=200005;
int n,m,k,s,t,vis[N],h[N];
int pre[N],f[N];
vector<int> e[N];
set<int> a[N];
void dfs(int u){
	for (int &v:e[u])
		if (!h[v]) {
			dfs(v);
			a[u].insert(f[v]);
		}
	for (int i=0;;++i)
		if (!a[u].count(i)) {
			f[u]=i;
			break;
		}
}
int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    cin>>n;
    for (int i=1;i<=n;++i){
		cin>>k;
		pre[i]=k;
		e[k].push_back(i);
	}
	int now=1;
	for (;!vis[now];now=pre[now]) vis[now]=1;
	for (;!h[now];now=pre[now]) h[now]=1;
	int mi=0x3f3f3f3f,mx=0,sum=0;
	for (int i=1;i<=n;++i)
		if (h[i]) {
			dfs(i);
			++sum;
			mi=min(mi,f[i]);
			mx=max(mx,f[i]);
		}
	if (mi==mx && (sum&1)) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
}
### 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>
#define ll long long
#define mod 998244353
using namespace std;
const int N=200005;
int n,m,k,s,t,vis[N],h[N];
int pre[N],f[N];
vector<int> e[N];
set<int> a[N];
void dfs(int u){
	for (int &v:e[u])
		if (!h[v]) {
			dfs(v);
			a[u].insert(f[v]);
		}
	for (int i=0;;++i)
		if (!a[u].count(i)) {
			f[u]=i;
			break;
		}
}
int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    cin>>n;
    for (int i=1;i<=n;++i){
		cin>>k;
		pre[i]=k;
		e[k].push_back(i);
	}
	int now=1;
	for (;!vis[now];now=pre[now]) vis[now]=1;
	for (;!h[now];now=pre[now]) h[now]=1;
	int mi=0x3f3f3f3f,mx=0,sum=0;
	for (int i=1;i<=n;++i)
		if (h[i]) {
			dfs(i);
			++sum;
			mi=min(mi,f[i]);
			mx=max(mx,f[i]);
		}
	if (mi==mx && (sum&1)) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
}
```