#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
using namespace std;
const int maxn=2e5;
int n,tot,cnt;
int pre[maxn+8],now[maxn+8],son[maxn+8];
bool vis[maxn+8],cir[maxn+8],inq[maxn+8];
int v[maxn+8],fa[maxn+8];

int read()
{
    int x=0,f=1;char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar()) if (ch=='-') f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
    return x*f;
}

void add(int u,int v)
{
    pre[++tot]=now[u];
    now[u]=tot;
    son[tot]=v;
}

void get(int x)
{
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    get(child);
	}
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    inq[v[child]]=1;
	}
    while(inq[v[x]]) v[x]++;
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    inq[v[child]]=0;
	}
}	    

int main()
{
    n=read();
    for (int i=1;i<=n;i++)
	{
	    fa[i]=read();
	    add(fa[i],i);
	}
    int x=1,mx=-inf,mn=inf;
    while(!vis[x]) vis[x]=1,x=fa[x];
    while(!cir[x]) cir[x]=1,x=fa[x];
    for (int i=1;i<=n;i++)
	if (cir[i])
	    {
		get(i),cnt++;
		mx=max(mx,v[i]);
		mn=min(mn,v[i]);
	    }
    mx==mn&&(cnt&1)?puts("IMPOSSIBLE"):puts("POSSIBLE");
    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<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
using namespace std;
const int maxn=2e5;
int n,tot,cnt;
int pre[maxn+8],now[maxn+8],son[maxn+8];
bool vis[maxn+8],cir[maxn+8],inq[maxn+8];
int v[maxn+8],fa[maxn+8];

int read()
{
    int x=0,f=1;char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar()) if (ch=='-') f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
    return x*f;
}

void add(int u,int v)
{
    pre[++tot]=now[u];
    now[u]=tot;
    son[tot]=v;
}

void get(int x)
{
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    get(child);
	}
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    inq[v[child]]=1;
	}
    while(inq[v[x]]) v[x]++;
    for (int p=now[x];p;p=pre[p])
	{
	    int child=son[p];
	    if (cir[child]) continue;
	    inq[v[child]]=0;
	}
}	    

int main()
{
    n=read();
    for (int i=1;i<=n;i++)
	{
	    fa[i]=read();
	    add(fa[i],i);
	}
    int x=1,mx=-inf,mn=inf;
    while(!vis[x]) vis[x]=1,x=fa[x];
    while(!cir[x]) cir[x]=1,x=fa[x];
    for (int i=1;i<=n;i++)
	if (cir[i])
	    {
		get(i),cnt++;
		mx=max(mx,v[i]);
		mn=min(mn,v[i]);
	    }
    mx==mn&&(cnt&1)?puts("IMPOSSIBLE"):puts("POSSIBLE");
    return 0;
}

```