#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const ll MOD = 1000000007LL;
int par[200000];
vector<int> out[200000];
int pos[200000];
set<int> s[200000];
int dfs(int v) {
	set<int> s;
	for (int to : out[v]) s.insert(dfs(to));
	int x = 0;
	while (s.find(x) != s.end()) x++;
	return x;
}
int main() {
	int N;
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> par[i];
		par[i]--;
		out[par[i]].push_back(i);
	}
	vector<int> vec;
	memset(pos, -1, sizeof(pos));
	pos[0] = 0;
	vec.push_back(0);
	int now = par[0];
	while (pos[now] == -1) {
		pos[now] = vec.size();
		vec.push_back(now);
		now = par[now];
	}
	int p = pos[now];
	for (int i = p; i < vec.size(); i++) {
		int prev;
		if (i == p) prev = vec.size() - 1;
		else prev = i - 1;
		for (int to : out[vec[i]]) {
			if (to == vec[prev]) continue;
			s[vec[i]].insert(dfs(to));
		}
	}
	vec.push_back(vec[p]);
	for (int i = 0; i <= out[vec[p]].size(); i++) {
		int x = i;
		for (int j = p + 1; j < vec.size(); j++) {
			int y = 0;
			while (y == x || s[vec[j]].find(y) != s[vec[j]].end()) y++;
			x = y;
		}
		if (x == i) {
			cout << "POSSIBLE" << endl;
			return 0;
		}
	}
	cout << "IMPOSSIBLE" << endl;
}

### Prompt

Please formulate 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;
typedef long long ll;
const ll MOD = 1000000007LL;
int par[200000];
vector<int> out[200000];
int pos[200000];
set<int> s[200000];
int dfs(int v) {
	set<int> s;
	for (int to : out[v]) s.insert(dfs(to));
	int x = 0;
	while (s.find(x) != s.end()) x++;
	return x;
}
int main() {
	int N;
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> par[i];
		par[i]--;
		out[par[i]].push_back(i);
	}
	vector<int> vec;
	memset(pos, -1, sizeof(pos));
	pos[0] = 0;
	vec.push_back(0);
	int now = par[0];
	while (pos[now] == -1) {
		pos[now] = vec.size();
		vec.push_back(now);
		now = par[now];
	}
	int p = pos[now];
	for (int i = p; i < vec.size(); i++) {
		int prev;
		if (i == p) prev = vec.size() - 1;
		else prev = i - 1;
		for (int to : out[vec[i]]) {
			if (to == vec[prev]) continue;
			s[vec[i]].insert(dfs(to));
		}
	}
	vec.push_back(vec[p]);
	for (int i = 0; i <= out[vec[p]].size(); i++) {
		int x = i;
		for (int j = p + 1; j < vec.size(); j++) {
			int y = 0;
			while (y == x || s[vec[j]].find(y) != s[vec[j]].end()) y++;
			x = y;
		}
		if (x == i) {
			cout << "POSSIBLE" << endl;
			return 0;
		}
	}
	cout << "IMPOSSIBLE" << endl;
}

```