#include <bits/stdc++.h>
using namespace std;

struct edge{int s,t,n;}e[200010];
int n,p[200010],h[200010],f[200010],vis[200010],c[200010],tim;
vector <int> V;

int go(int x)
{
	if (vis[x])  return x;
	vis[x]=1;
	return go(p[x]);
}

void dfs(int x)
{
	for (int i=h[x],y; y=e[i].t,i; i=e[i].n)
		if (!vis[y])  dfs(y);
	tim++;
	for (int i=h[x],y; y=e[i].t,i; i=e[i].n)
		if (!vis[y])  c[f[y]]=tim;
	for (f[x]=0; c[f[x]]==tim; f[x]++);
}

void work()
{
	scanf("%d",&n);
	for (int i=1; i<=n; i++)
		scanf("%d",&p[i]),e[i]=(edge){p[i],i,h[p[i]]},h[p[i]]=i;
	int x=go(1);
	memset(vis,0,sizeof(vis));
	do  V.push_back(x),vis[x]=1,x=p[x];  while (x!=V[0]);
	if (!(V.size()&1))  {puts("POSSIBLE");  return;}
	for (int i=0; i<V.size(); i++)  dfs(V[i]);
	V.push_back(x);
	for (int i=0; i<V.size()-1; i++)
		if (f[V[i]]!=f[V[i+1]])
			{puts("POSSIBLE");  return;}
	puts("IMPOSSIBLE");
}

int main()
{
	work();
	return 0;
}

### Prompt

Generate 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;

struct edge{int s,t,n;}e[200010];
int n,p[200010],h[200010],f[200010],vis[200010],c[200010],tim;
vector <int> V;

int go(int x)
{
	if (vis[x])  return x;
	vis[x]=1;
	return go(p[x]);
}

void dfs(int x)
{
	for (int i=h[x],y; y=e[i].t,i; i=e[i].n)
		if (!vis[y])  dfs(y);
	tim++;
	for (int i=h[x],y; y=e[i].t,i; i=e[i].n)
		if (!vis[y])  c[f[y]]=tim;
	for (f[x]=0; c[f[x]]==tim; f[x]++);
}

void work()
{
	scanf("%d",&n);
	for (int i=1; i<=n; i++)
		scanf("%d",&p[i]),e[i]=(edge){p[i],i,h[p[i]]},h[p[i]]=i;
	int x=go(1);
	memset(vis,0,sizeof(vis));
	do  V.push_back(x),vis[x]=1,x=p[x];  while (x!=V[0]);
	if (!(V.size()&1))  {puts("POSSIBLE");  return;}
	for (int i=0; i<V.size(); i++)  dfs(V[i]);
	V.push_back(x);
	for (int i=0; i<V.size()-1; i++)
		if (f[V[i]]!=f[V[i+1]])
			{puts("POSSIBLE");  return;}
	puts("IMPOSSIBLE");
}

int main()
{
	work();
	return 0;
}

```