#include<bits/stdc++.h>
using namespace std;

const int MAXN = 2.1e5;
int N;
int P[MAXN];
int inDeg[MAXN];
set<int> ch[MAXN];
int V[MAXN];
int main() {
  cin >> N;
  for (int i = 1; i <= N; i++) cin >> P[i];
  for (int i = 1; i <= N; i++) inDeg[P[i]] ++;
  vector<int> q;
  for (int i = 1; i <= N; i++) if (!inDeg[i]) q.push_back(i);
  for (int z = 0; z < int(q.size()); z++) {
    int i = q[z];
    V[i] = 0;
    while (ch[i].count(V[i])) V[i]++;
    ch[P[i]].insert(V[i]);
    if (!(--inDeg[P[i]])) q.push_back(P[i]);
  }
  
  int st = 1;
  while (!inDeg[st]) st++;
  vector<int> vals;
  int cur = 0;
  for (int z = 0; z < 3; z++) {
    for (int i = P[st]; true; i = P[i]) {
      int nxt = 0;
      while (nxt == cur || ch[i].count(nxt)) nxt++;
      cur = nxt;
      if (i == st) break;
    }
    vals.push_back(cur);
  }
  cout << (vals[1] == vals[2] ? "POSSIBLE" : "IMPOSSIBLE") << '\n';
}
### 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<bits/stdc++.h>
using namespace std;

const int MAXN = 2.1e5;
int N;
int P[MAXN];
int inDeg[MAXN];
set<int> ch[MAXN];
int V[MAXN];
int main() {
  cin >> N;
  for (int i = 1; i <= N; i++) cin >> P[i];
  for (int i = 1; i <= N; i++) inDeg[P[i]] ++;
  vector<int> q;
  for (int i = 1; i <= N; i++) if (!inDeg[i]) q.push_back(i);
  for (int z = 0; z < int(q.size()); z++) {
    int i = q[z];
    V[i] = 0;
    while (ch[i].count(V[i])) V[i]++;
    ch[P[i]].insert(V[i]);
    if (!(--inDeg[P[i]])) q.push_back(P[i]);
  }
  
  int st = 1;
  while (!inDeg[st]) st++;
  vector<int> vals;
  int cur = 0;
  for (int z = 0; z < 3; z++) {
    for (int i = P[st]; true; i = P[i]) {
      int nxt = 0;
      while (nxt == cur || ch[i].count(nxt)) nxt++;
      cur = nxt;
      if (i == st) break;
    }
    vals.push_back(cur);
  }
  cout << (vals[1] == vals[2] ? "POSSIBLE" : "IMPOSSIBLE") << '\n';
}
```