#include<bits/stdc++.h>
#define N 200009
using namespace std;

int n,rt,last,a[N],fa[N],fst[N],nxt[N],tg[N],f[N],g[N],bo[N];
void dfs(int x){
	int y;
	for (y=fst[x]; y; y=nxt[y]) if (!bo[y]) dfs(y);
	for (y=fst[x]; y; y=nxt[y]) if (!bo[y]) tg[f[y]]=x;
	for (y=0; tg[y]==x; y++);
	f[x]=y;
	for (y++; tg[y]==x; y++);
	g[x]=y;
}
int main(){
	scanf("%d",&n);
	int i;
	for (i=1; i<=n; i++){
		scanf("%d",&fa[i]);
		nxt[i]=fst[fa[i]]; fst[fa[i]]=i;
	}
	for (i=1; !bo[i]; i=fa[i]) bo[i]=1;
	memset(bo,0,sizeof(bo));
	for (; !bo[i]; i=fa[i]) bo[i]=1;
	rt=last=i;
	for (; bo[i]==1; last=i,i=fa[i]){ dfs(i); bo[i]=2; }
	for (a[rt]=f[rt],i=rt; fa[i]!=rt; i=fa[i])
		a[fa[i]]=(a[i]==f[fa[i]]?g[fa[i]]:f[fa[i]]);
	if (a[last]!=a[rt]){
		puts("POSSIBLE"); return 0;
	}
	for (a[rt]=g[rt],i=rt; fa[i]!=rt; i=fa[i])
		a[fa[i]]=(a[i]==f[fa[i]]?g[fa[i]]:f[fa[i]]);
	puts(a[last]==f[rt]?"POSSIBLE":"IMPOSSIBLE");
	return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 N 200009
using namespace std;

int n,rt,last,a[N],fa[N],fst[N],nxt[N],tg[N],f[N],g[N],bo[N];
void dfs(int x){
	int y;
	for (y=fst[x]; y; y=nxt[y]) if (!bo[y]) dfs(y);
	for (y=fst[x]; y; y=nxt[y]) if (!bo[y]) tg[f[y]]=x;
	for (y=0; tg[y]==x; y++);
	f[x]=y;
	for (y++; tg[y]==x; y++);
	g[x]=y;
}
int main(){
	scanf("%d",&n);
	int i;
	for (i=1; i<=n; i++){
		scanf("%d",&fa[i]);
		nxt[i]=fst[fa[i]]; fst[fa[i]]=i;
	}
	for (i=1; !bo[i]; i=fa[i]) bo[i]=1;
	memset(bo,0,sizeof(bo));
	for (; !bo[i]; i=fa[i]) bo[i]=1;
	rt=last=i;
	for (; bo[i]==1; last=i,i=fa[i]){ dfs(i); bo[i]=2; }
	for (a[rt]=f[rt],i=rt; fa[i]!=rt; i=fa[i])
		a[fa[i]]=(a[i]==f[fa[i]]?g[fa[i]]:f[fa[i]]);
	if (a[last]!=a[rt]){
		puts("POSSIBLE"); return 0;
	}
	for (a[rt]=g[rt],i=rt; fa[i]!=rt; i=fa[i])
		a[fa[i]]=(a[i]==f[fa[i]]?g[fa[i]]:f[fa[i]]);
	puts(a[last]==f[rt]?"POSSIBLE":"IMPOSSIBLE");
	return 0;
}

```