#include <bits/stdc++.h>

using namespace std;

const int INF = 1 << 30;

int N;
vector< int > g[200000], rg[200000];
int in[200000], grundy[200000];
bool notloop[200000];

int main()
{
  cin >> N;
  for(int i = 0; i < N; i++) {
    int p;
    cin >> p;
    g[--p].push_back(i);
    rg[i].push_back(p);
    ++in[p];
  }

  queue< int > que;

  for(int i = 0; i < N; i++) if(in[i] == 0) que.emplace(i);
  while(!que.empty()) {
    int p = que.front();
    notloop[p] = true;
    que.pop();
    set< int > st;
    for(auto &to : g[p]) st.emplace(grundy[to]);
    while(st.count(grundy[p])) ++grundy[p];
    for(auto &to : rg[p]) if(--in[to] == 0) que.emplace(to);
  }

  vector< int > vertex;
  set< int > qs;
  for(int i = 0; i < N; i++) if(!notloop[i]) vertex.push_back(i);
  for(int i : vertex) {
    set< int > st;
    for(auto &to : g[i]) if(notloop[to]) st.emplace(grundy[to]);
    while(st.count(grundy[i])) ++grundy[i];
    qs.emplace(grundy[i]);
  }
  if(vertex.size() % 2 == 1 && qs.size() == 1) cout << "IMPOSSIBLE" << endl;
  else cout << "POSSIBLE" << endl;
}

### Prompt

Generate a CPP solution 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 <bits/stdc++.h>

using namespace std;

const int INF = 1 << 30;

int N;
vector< int > g[200000], rg[200000];
int in[200000], grundy[200000];
bool notloop[200000];

int main()
{
  cin >> N;
  for(int i = 0; i < N; i++) {
    int p;
    cin >> p;
    g[--p].push_back(i);
    rg[i].push_back(p);
    ++in[p];
  }

  queue< int > que;

  for(int i = 0; i < N; i++) if(in[i] == 0) que.emplace(i);
  while(!que.empty()) {
    int p = que.front();
    notloop[p] = true;
    que.pop();
    set< int > st;
    for(auto &to : g[p]) st.emplace(grundy[to]);
    while(st.count(grundy[p])) ++grundy[p];
    for(auto &to : rg[p]) if(--in[to] == 0) que.emplace(to);
  }

  vector< int > vertex;
  set< int > qs;
  for(int i = 0; i < N; i++) if(!notloop[i]) vertex.push_back(i);
  for(int i : vertex) {
    set< int > st;
    for(auto &to : g[i]) if(notloop[to]) st.emplace(grundy[to]);
    while(st.count(grundy[i])) ++grundy[i];
    qs.emplace(grundy[i]);
  }
  if(vertex.size() % 2 == 1 && qs.size() == 1) cout << "IMPOSSIBLE" << endl;
  else cout << "POSSIBLE" << endl;
}

```