#define _USE_MATH_DEFINES
#include <cstdio>
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <complex>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <limits>
#include <climits>
#include <cfloat>
#include <functional>
#include <iterator>
using namespace std;

int getNum(const vector<int>& a, const vector<int>& to)
{
    set<int> s;
    for(int j : to)
        s.insert(a[j]);

    int ans = -1;
    if(s.empty() || *s.begin() != -1){
        ans = 0;
        for(int b : s){
            if(ans == b)
                ++ ans;
            else
                break;
        }
    }
    return ans;
}

int main()
{
    int n;
    cin >> n;
    vector<int> from(n);
    vector<vector<int> > to(n);
    for(int i=0; i<n; ++i){
        int p;
        cin >> p;
        -- p;
        from[i] = p;
        to[p].push_back(i);
    }

    queue<int> q;
    for(int i=0; i<n; ++i){
        if(to[i].empty())
            q.push(i);
    }
    vector<int> a(n, -1);
    while(!q.empty()){
        int i = q.front();
        q.pop();
        a[i] = getNum(a, to[i]);
        if(a[i] != -1)
            q.push(from[i]);
    }

    int initPos = 0;
    while(a[initPos] != -1)
        ++ initPos;
    for(int initVal=0; initVal<50; ++initVal){
        int i = initPos;
        a[i] = initVal;
        do{
            i = from[i];
            a[i] = getNum(a, to[i]);
        }while(i != initPos);

        if(a[i] == initVal){
            cout << "POSSIBLE" << endl;
            return 0;
        }
    }

    cout << "IMPOSSIBLE" << endl;
    return 0;
}

### Prompt

Please provide a CPP coded solution 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
#define _USE_MATH_DEFINES
#include <cstdio>
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <complex>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <limits>
#include <climits>
#include <cfloat>
#include <functional>
#include <iterator>
using namespace std;

int getNum(const vector<int>& a, const vector<int>& to)
{
    set<int> s;
    for(int j : to)
        s.insert(a[j]);

    int ans = -1;
    if(s.empty() || *s.begin() != -1){
        ans = 0;
        for(int b : s){
            if(ans == b)
                ++ ans;
            else
                break;
        }
    }
    return ans;
}

int main()
{
    int n;
    cin >> n;
    vector<int> from(n);
    vector<vector<int> > to(n);
    for(int i=0; i<n; ++i){
        int p;
        cin >> p;
        -- p;
        from[i] = p;
        to[p].push_back(i);
    }

    queue<int> q;
    for(int i=0; i<n; ++i){
        if(to[i].empty())
            q.push(i);
    }
    vector<int> a(n, -1);
    while(!q.empty()){
        int i = q.front();
        q.pop();
        a[i] = getNum(a, to[i]);
        if(a[i] != -1)
            q.push(from[i]);
    }

    int initPos = 0;
    while(a[initPos] != -1)
        ++ initPos;
    for(int initVal=0; initVal<50; ++initVal){
        int i = initPos;
        a[i] = initVal;
        do{
            i = from[i];
            a[i] = getNum(a, to[i]);
        }while(i != initPos);

        if(a[i] == initVal){
            cout << "POSSIBLE" << endl;
            return 0;
        }
    }

    cout << "IMPOSSIBLE" << endl;
    return 0;
}

```