#include<cstdio>
#include<cctype>
#include<cstring>
#include<algorithm>
using namespace std;
int n,cnt,tot,mini=0x7f7f7f7f,maxn,f[200010],vis[200010],sg[200010],head[200010],nxt[200010],to[200010];
bool iscir[200010];
void add_edge(int u,int v){
	nxt[++tot]=head[u];
	to[tot]=v;
	head[u]=tot;
	return;
}
void dfs(int u){
	for(int i=head[u];~i;i=nxt[i])
		if(!iscir[to[i]])
			dfs(to[i]);
	for(int i=head[u];~i;i=nxt[i])
		if(!iscir[to[i]])
			vis[sg[to[i]]]=1;
	for(sg[u]=0;vis[sg[u]];sg[u]++);
	for(int i=head[u];~i;i=nxt[i])
		vis[sg[to[i]]]=0;
	return;
}
void find_cir(){
	for(int i=1;vis[i]<=1;i=f[i]){
		vis[i]++;
		if(vis[i]==2){
			iscir[i]=1;
			++cnt;
		}
	}
	return;
}
char buffer[10000010],*hd;
char Getchar(){
	return *hd++;
}
int rd(){
	int x=0;
	char c;
	do c=Getchar();
	while(!isdigit(c));
	do{
		x=(x<<1)+(x<<3)+(c^48);
		c=Getchar();
	}while(isdigit(c));
	return x;
}
int main(){
	fread(buffer,1,10000000,stdin);
	hd=buffer;
	memset(head,-1,sizeof(head));
	n=rd();
	for(int i=1;i<=n;i++)
		add_edge(f[i]=rd(),i);
	find_cir();
	if(!(cnt&1)){
		puts("POSSIBLE");
		return 0;
	}
	memset(vis,0,sizeof(vis));
	for(int i=1;i<=n;i++){
		if(iscir[i]){
			dfs(i);
			maxn=max(maxn,sg[i]);
			mini=min(mini,sg[i]);
		}
	}
	if(maxn!=mini)
		puts("POSSIBLE");
	else puts("IMPOSSIBLE");
	return 0;
}
### Prompt

Create a solution in cpp for 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<cstdio>
#include<cctype>
#include<cstring>
#include<algorithm>
using namespace std;
int n,cnt,tot,mini=0x7f7f7f7f,maxn,f[200010],vis[200010],sg[200010],head[200010],nxt[200010],to[200010];
bool iscir[200010];
void add_edge(int u,int v){
	nxt[++tot]=head[u];
	to[tot]=v;
	head[u]=tot;
	return;
}
void dfs(int u){
	for(int i=head[u];~i;i=nxt[i])
		if(!iscir[to[i]])
			dfs(to[i]);
	for(int i=head[u];~i;i=nxt[i])
		if(!iscir[to[i]])
			vis[sg[to[i]]]=1;
	for(sg[u]=0;vis[sg[u]];sg[u]++);
	for(int i=head[u];~i;i=nxt[i])
		vis[sg[to[i]]]=0;
	return;
}
void find_cir(){
	for(int i=1;vis[i]<=1;i=f[i]){
		vis[i]++;
		if(vis[i]==2){
			iscir[i]=1;
			++cnt;
		}
	}
	return;
}
char buffer[10000010],*hd;
char Getchar(){
	return *hd++;
}
int rd(){
	int x=0;
	char c;
	do c=Getchar();
	while(!isdigit(c));
	do{
		x=(x<<1)+(x<<3)+(c^48);
		c=Getchar();
	}while(isdigit(c));
	return x;
}
int main(){
	fread(buffer,1,10000000,stdin);
	hd=buffer;
	memset(head,-1,sizeof(head));
	n=rd();
	for(int i=1;i<=n;i++)
		add_edge(f[i]=rd(),i);
	find_cir();
	if(!(cnt&1)){
		puts("POSSIBLE");
		return 0;
	}
	memset(vis,0,sizeof(vis));
	for(int i=1;i<=n;i++){
		if(iscir[i]){
			dfs(i);
			maxn=max(maxn,sg[i]);
			mini=min(mini,sg[i]);
		}
	}
	if(maxn!=mini)
		puts("POSSIBLE");
	else puts("IMPOSSIBLE");
	return 0;
}
```