#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int MAXN = 1000100;

int N;
int arr[MAXN];
int pprev[MAXN];
vector <int> nnext[MAXN];
int res[MAXN];

bool spec[MAXN];
set <int> s[MAXN];

int gmex (int i, int opt)
{
    int ans = 0;
    while (ans == opt || s[i].find(ans) != s[i].end())
        ans++;
    return ans;
}

void flood (int cloc)
{
    for (int neigh : nnext[cloc])
        if (!spec[neigh])
        {
            flood (neigh);
            s[cloc].insert(res[neigh]);
        }
    res[cloc] = 0;
    while (s[cloc].find(res[cloc]) != s[cloc].end())
        res[cloc]++;
}

bool gogo (int cloc)
{
    int cr = res[cloc];
    int cstart = cloc;
    do
    {
        int cprev = pprev[cloc];
        res[cprev] = gmex (cprev, res[cloc]);
        cloc = cprev;
    } while (cloc != cstart);
    return cr == res[cstart];
}

int main()
{
    ios_base::sync_with_stdio(0);

    cin >> N;
    for (int i = 0; i < N; i++)
    {
        cin >> arr[i];
        arr[i]--;
        pprev[i] = arr[i];
        nnext[arr[i]].push_back(i);
    }

    int cloc = 0;
    for (int i = 0; i < N; i++)
        cloc = pprev[cloc];

    while (!spec[cloc])
    {
        spec[cloc] = true;
        cloc = pprev[cloc];
    }

    for (int i = 0; i < N; i++)
        if (spec[i]) flood (i);

    int clo = res[cloc];
    if (gogo (cloc))
    {
        cout << "POSSIBLE\n";
        return 0;
    }
    res[cloc] = gmex (cloc, clo);
    if (gogo (cloc))
    {
        cout << "POSSIBLE\n";
        return 0;
    }
    cout << "IMPOSSIBLE\n";
}
### 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 <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int MAXN = 1000100;

int N;
int arr[MAXN];
int pprev[MAXN];
vector <int> nnext[MAXN];
int res[MAXN];

bool spec[MAXN];
set <int> s[MAXN];

int gmex (int i, int opt)
{
    int ans = 0;
    while (ans == opt || s[i].find(ans) != s[i].end())
        ans++;
    return ans;
}

void flood (int cloc)
{
    for (int neigh : nnext[cloc])
        if (!spec[neigh])
        {
            flood (neigh);
            s[cloc].insert(res[neigh]);
        }
    res[cloc] = 0;
    while (s[cloc].find(res[cloc]) != s[cloc].end())
        res[cloc]++;
}

bool gogo (int cloc)
{
    int cr = res[cloc];
    int cstart = cloc;
    do
    {
        int cprev = pprev[cloc];
        res[cprev] = gmex (cprev, res[cloc]);
        cloc = cprev;
    } while (cloc != cstart);
    return cr == res[cstart];
}

int main()
{
    ios_base::sync_with_stdio(0);

    cin >> N;
    for (int i = 0; i < N; i++)
    {
        cin >> arr[i];
        arr[i]--;
        pprev[i] = arr[i];
        nnext[arr[i]].push_back(i);
    }

    int cloc = 0;
    for (int i = 0; i < N; i++)
        cloc = pprev[cloc];

    while (!spec[cloc])
    {
        spec[cloc] = true;
        cloc = pprev[cloc];
    }

    for (int i = 0; i < N; i++)
        if (spec[i]) flood (i);

    int clo = res[cloc];
    if (gogo (cloc))
    {
        cout << "POSSIBLE\n";
        return 0;
    }
    res[cloc] = gmex (cloc, clo);
    if (gogo (cloc))
    {
        cout << "POSSIBLE\n";
        return 0;
    }
    cout << "IMPOSSIBLE\n";
}
```