#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>

int a[200005],n,Fa[200005],Cnt,Maxv,Minv=2147483647;
bool Vis[200005],b[25];
std::vector<int> g[200005];

void DFS(const int x)
{
    for(int y:g[x])if(!Vis[y])DFS(y);
    for(int y:g[x])if(!Vis[y])b[a[y]]=true;
    while(b[a[x]])++a[x];
    for(int y:g[x])if(!Vis[y])b[a[y]]=false;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&Fa[i]),g[Fa[i]].push_back(i);
    int x=1;
    while(!Vis[x=Fa[x]])Vis[x]=true;
    memset(Vis,false,sizeof Vis);
    while(!Vis[x=Fa[x]])Vis[x]=true;
    for(int i=1;i<=n;++i)if(Vis[i])DFS(i),++Cnt,Maxv=std::max(Maxv,a[i]),Minv=std::min(Minv,a[i]);
    puts(Maxv!=Minv||Cnt%2==0?"POSSIBLE":"IMPOSSIBLE");
    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 <vector>
#include <cstring>
#include <algorithm>

int a[200005],n,Fa[200005],Cnt,Maxv,Minv=2147483647;
bool Vis[200005],b[25];
std::vector<int> g[200005];

void DFS(const int x)
{
    for(int y:g[x])if(!Vis[y])DFS(y);
    for(int y:g[x])if(!Vis[y])b[a[y]]=true;
    while(b[a[x]])++a[x];
    for(int y:g[x])if(!Vis[y])b[a[y]]=false;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&Fa[i]),g[Fa[i]].push_back(i);
    int x=1;
    while(!Vis[x=Fa[x]])Vis[x]=true;
    memset(Vis,false,sizeof Vis);
    while(!Vis[x=Fa[x]])Vis[x]=true;
    for(int i=1;i<=n;++i)if(Vis[i])DFS(i),++Cnt,Maxv=std::max(Maxv,a[i]),Minv=std::min(Minv,a[i]);
    puts(Maxv!=Minv||Cnt%2==0?"POSSIBLE":"IMPOSSIBLE");
    return 0;
}
```