#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#define maxn 200010
using namespace std;
int read()
{
    int x=0,f=1;
    char ch=getchar();
    while(ch-'0'<0||ch-'0'>9){if(ch=='-') f=-1;ch=getchar();}
    while(ch-'0'>=0&&ch-'0'<=9){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int n;
int pre[maxn],deg[maxn];
queue<int>q;
int a[maxn],vis[maxn];
int book[maxn];
int head[maxn],nxt[maxn],to[maxn],tot;
void add(int u,int v)
{
    tot++;
    nxt[tot]=head[u];
    head[u]=tot;
    to[tot]=v;
}
int cnt;
int main()
{
    n=read();
    for(int i=1;i<=n;i++)
    {
        pre[i]=read();
        add(pre[i],i);
        deg[pre[i]]++;
    }
    for(int i=1;i<=n;i++)
      if(!deg[i])  q.push(i);
    while(q.size())
    {
        int now=q.front();
        book[now]=1;
        cnt++;
        q.pop();
        deg[pre[now]]--;
        if(!deg[pre[now]])  q.push(pre[now]);
        for(int i=head[now];i;i=nxt[i])  vis[a[to[i]]]=now;
        while(vis[a[now]]==now)  a[now]++;
    }
    if((n-cnt)%2==0)
    {
        puts("POSSIBLE");
        return 0;
    }
    int las=-1;
    for(int i=1;i<=n;i++)
    {
        if(book[i])  continue;
        for(int j=head[i];j;j=nxt[j])
          if(book[to[j]])  vis[a[to[j]]]=i;
        int tmp=0;
        while(vis[tmp]==i)  tmp++;
        if(las==-1)  las=tmp;
        else{
            if(las!=tmp)
            {
                puts("POSSIBLE");
                return 0;
            }
        }
    }
    puts("IMPOSSIBLE");
    return 0;
}
### Prompt

In CPP, your task is to solve 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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#define maxn 200010
using namespace std;
int read()
{
    int x=0,f=1;
    char ch=getchar();
    while(ch-'0'<0||ch-'0'>9){if(ch=='-') f=-1;ch=getchar();}
    while(ch-'0'>=0&&ch-'0'<=9){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int n;
int pre[maxn],deg[maxn];
queue<int>q;
int a[maxn],vis[maxn];
int book[maxn];
int head[maxn],nxt[maxn],to[maxn],tot;
void add(int u,int v)
{
    tot++;
    nxt[tot]=head[u];
    head[u]=tot;
    to[tot]=v;
}
int cnt;
int main()
{
    n=read();
    for(int i=1;i<=n;i++)
    {
        pre[i]=read();
        add(pre[i],i);
        deg[pre[i]]++;
    }
    for(int i=1;i<=n;i++)
      if(!deg[i])  q.push(i);
    while(q.size())
    {
        int now=q.front();
        book[now]=1;
        cnt++;
        q.pop();
        deg[pre[now]]--;
        if(!deg[pre[now]])  q.push(pre[now]);
        for(int i=head[now];i;i=nxt[i])  vis[a[to[i]]]=now;
        while(vis[a[now]]==now)  a[now]++;
    }
    if((n-cnt)%2==0)
    {
        puts("POSSIBLE");
        return 0;
    }
    int las=-1;
    for(int i=1;i<=n;i++)
    {
        if(book[i])  continue;
        for(int j=head[i];j;j=nxt[j])
          if(book[to[j]])  vis[a[to[j]]]=i;
        int tmp=0;
        while(vis[tmp]==i)  tmp++;
        if(las==-1)  las=tmp;
        else{
            if(las!=tmp)
            {
                puts("POSSIBLE");
                return 0;
            }
        }
    }
    puts("IMPOSSIBLE");
    return 0;
}
```