#include<bits/stdc++.h>
#include<vector>
#define N 200005
using namespace std;
int n,f[N],a[N],w[N],lw,vis[N],vr[N],cnt;
vector<int> G[N];
void dfs(int t)
{
	int i;
	for(i=0;i<G[t].size();i++)
		if(!vis[G[t][i]]) dfs(G[t][i]);
	++cnt;
	for(i=0;i<G[t].size();i++)
		if(!vis[G[t][i]]) vr[a[G[t][i]]]=cnt;
	for(i=0;vr[i]==cnt;i++);
	a[t]=i;
}
int main()
{
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%d",&f[i]);
	for(i=1;!vis[i];i=f[i]) vis[i]=1;
	memset(vis,0,sizeof(vis));
	for(;!vis[i];i=f[i]) vis[i]=1;
	for(i=1;i<=n;i++) if(vis[i]) w[++lw]=i;
	for(i=1;i<=n;i++) G[f[i]].push_back(i);
	for(i=1;i<=lw;i++) dfs(w[i]);
	for(i=2;i<=lw;i++)
		if(a[w[i]]!=a[w[i-1]]) break;
	if(i>lw&&(lw&1)) printf("IMPOSSIBLE");
	else printf("POSSIBLE");
	return 0;
}

### Prompt

Please create a solution in CPP 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>
#include<vector>
#define N 200005
using namespace std;
int n,f[N],a[N],w[N],lw,vis[N],vr[N],cnt;
vector<int> G[N];
void dfs(int t)
{
	int i;
	for(i=0;i<G[t].size();i++)
		if(!vis[G[t][i]]) dfs(G[t][i]);
	++cnt;
	for(i=0;i<G[t].size();i++)
		if(!vis[G[t][i]]) vr[a[G[t][i]]]=cnt;
	for(i=0;vr[i]==cnt;i++);
	a[t]=i;
}
int main()
{
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%d",&f[i]);
	for(i=1;!vis[i];i=f[i]) vis[i]=1;
	memset(vis,0,sizeof(vis));
	for(;!vis[i];i=f[i]) vis[i]=1;
	for(i=1;i<=n;i++) if(vis[i]) w[++lw]=i;
	for(i=1;i<=n;i++) G[f[i]].push_back(i);
	for(i=1;i<=lw;i++) dfs(w[i]);
	for(i=2;i<=lw;i++)
		if(a[w[i]]!=a[w[i-1]]) break;
	if(i>lw&&(lw&1)) printf("IMPOSSIBLE");
	else printf("POSSIBLE");
	return 0;
}

```