#include<cstdio>
#include<algorithm>
using namespace std;
const int N=2e5+5;
int n,i,fa[N],dg[N],a[N],h,t,q[N];
int et,he[N],cnt,hv[N];
struct edge{int l,v;}e[N];
int read(){
	char c=getchar();int k=0;for (;c<48||c>57;c=getchar());
	for (;c>47&&c<58;c=getchar()) k=(k<<3)+(k<<1)+c-48;return k;
}
int get(int x){
	cnt++;int i;
	for (i=he[x];i;i=e[i].l) hv[e[i].v]=cnt;
	for (i=0;hv[i]==cnt;i++);return i;
}
int main(){
	for (n=read(),i=1;i<=n;i++)
		dg[fa[i]=read()]++;
	for (i=1;i<=n;i++) if (!dg[i]) q[++t]=i;
	while (h!=t){
		int x=q[++h],y=fa[x];a[x]=get(x);
		e[++et].l=he[y];he[y]=et;e[et].v=a[x];
		if (!(--dg[y])) q[++t]=y;
	}
	if (!((n-t)&1)){puts("POSSIBLE");return 0;}
	int k=-1;
	for (i=1;i<=n;i++) if (dg[i]){
		int v=get(i);if (k==-1) k=v;
		if (k!=v) break;
	}
	puts(i<=n?"POSSIBLE":"IMPOSSIBLE");
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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<algorithm>
using namespace std;
const int N=2e5+5;
int n,i,fa[N],dg[N],a[N],h,t,q[N];
int et,he[N],cnt,hv[N];
struct edge{int l,v;}e[N];
int read(){
	char c=getchar();int k=0;for (;c<48||c>57;c=getchar());
	for (;c>47&&c<58;c=getchar()) k=(k<<3)+(k<<1)+c-48;return k;
}
int get(int x){
	cnt++;int i;
	for (i=he[x];i;i=e[i].l) hv[e[i].v]=cnt;
	for (i=0;hv[i]==cnt;i++);return i;
}
int main(){
	for (n=read(),i=1;i<=n;i++)
		dg[fa[i]=read()]++;
	for (i=1;i<=n;i++) if (!dg[i]) q[++t]=i;
	while (h!=t){
		int x=q[++h],y=fa[x];a[x]=get(x);
		e[++et].l=he[y];he[y]=et;e[et].v=a[x];
		if (!(--dg[y])) q[++t]=y;
	}
	if (!((n-t)&1)){puts("POSSIBLE");return 0;}
	int k=-1;
	for (i=1;i<=n;i++) if (dg[i]){
		int v=get(i);if (k==-1) k=v;
		if (k!=v) break;
	}
	puts(i<=n?"POSSIBLE":"IMPOSSIBLE");
}
```