#include<bits/stdc++.h>
#define pii pair<int, int>
#define fir first
#define sec second
#define ll long long
using namespace std;
const int MAXN = 2e5 + 7;
int n, p[MAXN], val[MAXN], cnt[MAXN];
pii e;
bool vis[MAXN];
vector<int>G[MAXN];
int getmex(int u)
{
    int res = 0;
    for (int v : G[u]) if (val[v] != -1) cnt[val[v]]++;
    for (int x = 0; x <= n; x++) if (cnt[x] == 0)
    {
        res = x;
        break;
    }
    for (int v : G[u]) if (val[v] != -1) cnt[val[v]]--;
    return res;
}
void dfs(int u)
{
    vis[u] = 1;
    for (int v : G[u])
    {
        if (vis[v]) 
        {
            if (val[v] == -1) e = {u, v};
            continue; 
        }
        dfs(v);
    }
    val[u] = getmex(u);
}
int main() 
{
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) 
    {
        scanf("%d", &p[i]);
        G[p[i]].push_back(i);
    }
    memset(val, -1, sizeof(val));
    for (int i = 1; i <= n; i++) if (val[i] == -1) dfs(i);
    val[e.fir] = getmex(e.fir);
    int u = p[e.fir];
    while (u != e.fir)
    {
        val[u] = getmex(u);
        u = p[u];
    } 
    if (getmex(e.fir) == val[e.fir]) puts("POSSIBLE");
    else puts("IMPOSSIBLE");
    
    return 0;
}
### 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>
#define pii pair<int, int>
#define fir first
#define sec second
#define ll long long
using namespace std;
const int MAXN = 2e5 + 7;
int n, p[MAXN], val[MAXN], cnt[MAXN];
pii e;
bool vis[MAXN];
vector<int>G[MAXN];
int getmex(int u)
{
    int res = 0;
    for (int v : G[u]) if (val[v] != -1) cnt[val[v]]++;
    for (int x = 0; x <= n; x++) if (cnt[x] == 0)
    {
        res = x;
        break;
    }
    for (int v : G[u]) if (val[v] != -1) cnt[val[v]]--;
    return res;
}
void dfs(int u)
{
    vis[u] = 1;
    for (int v : G[u])
    {
        if (vis[v]) 
        {
            if (val[v] == -1) e = {u, v};
            continue; 
        }
        dfs(v);
    }
    val[u] = getmex(u);
}
int main() 
{
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) 
    {
        scanf("%d", &p[i]);
        G[p[i]].push_back(i);
    }
    memset(val, -1, sizeof(val));
    for (int i = 1; i <= n; i++) if (val[i] == -1) dfs(i);
    val[e.fir] = getmex(e.fir);
    int u = p[e.fir];
    while (u != e.fir)
    {
        val[u] = getmex(u);
        u = p[u];
    } 
    if (getmex(e.fir) == val[e.fir]) puts("POSSIBLE");
    else puts("IMPOSSIBLE");
    
    return 0;
}
```