#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i, x, n) for (int i = x; i < (int)(n); ++i)

vector<int> g[200001];
pair<int, int> c[200001];
int vis[200001], R, expc;

inline int mux(set<int> &st){
	int i = 0;
	for (set<int>::iterator it = st.begin(); it != st.end(); ++it){
		if (i == *it)++i;
		else return i;
	}
	return i;
}

void go(int v){
	vis[v] = 1;
	set<int> st1, st2;
	bool bad = false;
	f(i, 0, g[v].size()){
		int u = g[v][i];
		if (vis[u] == 1){
			R = u;
			bad = true;
			continue;
		}
		if (vis[u] == 0)go(u);
		st1.insert(c[u].first);
		st2.insert(c[u].second);
	}
	c[v] = make_pair(mux(st1), mux(st2));
	if (bad)++c[v].second, expc = c[v].first;
	vis[v] = 2;
}

int main(){
	int n;
	scanf("%d", &n);
	f(i, 1, n + 1){
		int t;
		scanf("%d", &t);
		g[t].push_back(i);
	}
	f(i, 1, n + 1)if (vis[i] == 0)go(i);
	if (R == 0 || c[R].first != expc || c[R].second == expc)printf("POSSIBLE\n");
	else printf("IMPOSSIBLE\n");
}
### Prompt

In CPP, your task is to solve 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;
#define ll long long
#define f(i, x, n) for (int i = x; i < (int)(n); ++i)

vector<int> g[200001];
pair<int, int> c[200001];
int vis[200001], R, expc;

inline int mux(set<int> &st){
	int i = 0;
	for (set<int>::iterator it = st.begin(); it != st.end(); ++it){
		if (i == *it)++i;
		else return i;
	}
	return i;
}

void go(int v){
	vis[v] = 1;
	set<int> st1, st2;
	bool bad = false;
	f(i, 0, g[v].size()){
		int u = g[v][i];
		if (vis[u] == 1){
			R = u;
			bad = true;
			continue;
		}
		if (vis[u] == 0)go(u);
		st1.insert(c[u].first);
		st2.insert(c[u].second);
	}
	c[v] = make_pair(mux(st1), mux(st2));
	if (bad)++c[v].second, expc = c[v].first;
	vis[v] = 2;
}

int main(){
	int n;
	scanf("%d", &n);
	f(i, 1, n + 1){
		int t;
		scanf("%d", &t);
		g[t].push_back(i);
	}
	f(i, 1, n + 1)if (vis[i] == 0)go(i);
	if (R == 0 || c[R].first != expc || c[R].second == expc)printf("POSSIBLE\n");
	else printf("IMPOSSIBLE\n");
}
```