#include<bits/stdc++.h>

using namespace std;

const int N=200005;

vector<int>e[N];
set<int>D[N];
bool in[N],vi[N];
int sg[N],sg2[N],n,p[N];

void dfs(int x){
	for(int v:e[x])if(!in[v])dfs(v),D[x].insert(sg[v]);
	while(D[x].count(sg[x]))sg[x]++;
}

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&p[i]),e[p[i]].push_back(i);
	int x=1;
	while(!vi[x])vi[x]=true,x=p[x];
	in[x]=true;
	for(int y=p[x];y!=x;y=p[y])in[y]=true;
	for(int i=1;i<=n;i++)if(in[i]){
		dfs(i);
		sg2[i]=sg[i]+1;
		while(D[i].count(sg2[i]))sg2[i]++;
	}
	int cur=sg[x];
	for(int y=p[x];y!=x;y=p[y])if(cur==sg[y])cur=sg2[y];else cur=sg[y];
	if(cur!=sg[x])puts("POSSIBLE"),exit(0);
	cur=sg2[x];
	for(int y=p[x];y!=x;y=p[y])if(cur==sg[y])cur=sg2[y];else cur=sg[y];
	if(cur==sg[x])puts("POSSIBLE"),exit(0);
	puts("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>

using namespace std;

const int N=200005;

vector<int>e[N];
set<int>D[N];
bool in[N],vi[N];
int sg[N],sg2[N],n,p[N];

void dfs(int x){
	for(int v:e[x])if(!in[v])dfs(v),D[x].insert(sg[v]);
	while(D[x].count(sg[x]))sg[x]++;
}

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&p[i]),e[p[i]].push_back(i);
	int x=1;
	while(!vi[x])vi[x]=true,x=p[x];
	in[x]=true;
	for(int y=p[x];y!=x;y=p[y])in[y]=true;
	for(int i=1;i<=n;i++)if(in[i]){
		dfs(i);
		sg2[i]=sg[i]+1;
		while(D[i].count(sg2[i]))sg2[i]++;
	}
	int cur=sg[x];
	for(int y=p[x];y!=x;y=p[y])if(cur==sg[y])cur=sg2[y];else cur=sg[y];
	if(cur!=sg[x])puts("POSSIBLE"),exit(0);
	cur=sg2[x];
	for(int y=p[x];y!=x;y=p[y])if(cur==sg[y])cur=sg2[y];else cur=sg[y];
	if(cur==sg[x])puts("POSSIBLE"),exit(0);
	puts("IMPOSSIBLE");
	return 0;
}
```