#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N = 200050;
template<typename T>
inline void read(T&x)
{
	T f = 1,c = 0;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){c=c*10+ch-'0';ch=getchar();}
	x = f*c;
}
int n,fa[N],hed[N],cnt;
struct EG
{
	int to,nxt;
}e[N];
void ae(int f,int t)
{
	e[++cnt].to = t;
	e[cnt].nxt = hed[f];
	hed[f] = cnt;
}
bool cir[N];
int sta[N],tl;
void get_cir()
{
	int u = 1;
	while(!cir[u])cir[u]=1,u=fa[u];
	memset(cir,0,sizeof(cir));
	while(!cir[u])sta[++tl]=u,cir[u]=1,u=fa[u];
}
int sg[N];
int vis[N],tim;
void dfs(int u)
{
	for(int j=hed[u];j;j=e[j].nxt)
	{
		int to = e[j].to;
		if(!cir[to])dfs(to);
	}
	tim++;
	for(int j=hed[u];j;j=e[j].nxt)
	{
		int to = e[j].to;
		if(!cir[to])vis[sg[to]]=tim;
	}
	sg[u]=0;
	while(vis[sg[u]]==tim)sg[u]++;
}
int main()
{
	read(n);
	for(int i=1;i<=n;i++)
	{
		read(fa[i]);
		ae(fa[i],i);
	}
	get_cir();
	int mx = -1,mn = n+1;
	for(int i=1;i<=tl;i++)
		dfs(sta[i]),mx=max(mx,sg[sta[i]]),mn=min(mn,sg[sta[i]]);
	if(mx==mn&&(tl&1))puts("IMPOSSIBLE");
	else puts("POSSIBLE");
	return 0;
}

### Prompt

Please create a solution in Cpp 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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N = 200050;
template<typename T>
inline void read(T&x)
{
	T f = 1,c = 0;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){c=c*10+ch-'0';ch=getchar();}
	x = f*c;
}
int n,fa[N],hed[N],cnt;
struct EG
{
	int to,nxt;
}e[N];
void ae(int f,int t)
{
	e[++cnt].to = t;
	e[cnt].nxt = hed[f];
	hed[f] = cnt;
}
bool cir[N];
int sta[N],tl;
void get_cir()
{
	int u = 1;
	while(!cir[u])cir[u]=1,u=fa[u];
	memset(cir,0,sizeof(cir));
	while(!cir[u])sta[++tl]=u,cir[u]=1,u=fa[u];
}
int sg[N];
int vis[N],tim;
void dfs(int u)
{
	for(int j=hed[u];j;j=e[j].nxt)
	{
		int to = e[j].to;
		if(!cir[to])dfs(to);
	}
	tim++;
	for(int j=hed[u];j;j=e[j].nxt)
	{
		int to = e[j].to;
		if(!cir[to])vis[sg[to]]=tim;
	}
	sg[u]=0;
	while(vis[sg[u]]==tim)sg[u]++;
}
int main()
{
	read(n);
	for(int i=1;i<=n;i++)
	{
		read(fa[i]);
		ae(fa[i],i);
	}
	get_cir();
	int mx = -1,mn = n+1;
	for(int i=1;i<=tl;i++)
		dfs(sta[i]),mx=max(mx,sg[sta[i]]),mn=min(mn,sg[sta[i]]);
	if(mx==mn&&(tl&1))puts("IMPOSSIBLE");
	else puts("POSSIBLE");
	return 0;
}

```