#include <iostream>
#include <vector>
#include <memory.h>
using namespace std;

vector<vector<int>> edge;
int visited[200010];
bool cycle[200010];
int grundy[200010];
vector<int> cyc;

bool dfs(int i) {
	visited[i] = 1;
	for (int u: edge[i]) {
		if (visited[u] == 0) cycle[i] |= dfs(u);
		else if (visited[u] == 1) cycle[i] = 1;
	}
	visited[i] = 2;
	if (cycle[i]) cyc.push_back(i);
	return cycle[i];
}

int find_grundy(int i) {
	if (grundy[i] != -1) return grundy[i];
	int mask = 0;
	for (int u: edge[i]) {
		mask |= (1 << find_grundy(u));
	}
	return grundy[i] = __builtin_ctz(~mask);
}

int grundy_single_init(int i) {
	int mask = 0;
	for (int u: edge[i]) {
		if (!cycle[u]) mask |= (1 << grundy[u]);
	}
	return mask;
}

int grundy_single(int i) {
	int mask = 0;
	for (int u: edge[i]) {
		mask |= (1 << grundy[u]);
	}
	return __builtin_ctz(~mask);
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	int n, t;
	cin >> n;

	edge.resize(n);
	memset(grundy, -1, sizeof(grundy));
	for (int i = 0; i < n; ++i) {
		cin >> t;
		t--;
		edge[t].push_back(i);
	}

	for (int i = 0; i < n; ++i) {
		if (!visited[i]) dfs(i);
	}

	for (int i = 0; i < n; ++i) {
		if (!cycle[i] && grundy[i] == -1) find_grundy(i);
	}

	int start = grundy_single_init(cyc[0]);
	int low = __builtin_ctz(~start);
	grundy[cyc[0]] = low;
	start |= (1 << low);
	for (int i = 1; i < cyc.size(); ++i) {
		grundy[cyc[i]] = grundy_single(cyc[i]);
	}
	if (grundy_single(cyc[0]) == grundy[cyc[0]]) {
		cout << "POSSIBLE";
		return 0;
	}
		
	grundy[cyc[0]] = __builtin_ctz(~start);
	for (int i = 1; i < cyc.size(); ++i) {
		grundy[cyc[i]] = grundy_single(cyc[i]);
	}
	if (grundy_single(cyc[0]) == grundy[cyc[0]]) {
		cout << "POSSIBLE";
	}
	else cout << "IMPOSSIBLE";
}
### 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 <iostream>
#include <vector>
#include <memory.h>
using namespace std;

vector<vector<int>> edge;
int visited[200010];
bool cycle[200010];
int grundy[200010];
vector<int> cyc;

bool dfs(int i) {
	visited[i] = 1;
	for (int u: edge[i]) {
		if (visited[u] == 0) cycle[i] |= dfs(u);
		else if (visited[u] == 1) cycle[i] = 1;
	}
	visited[i] = 2;
	if (cycle[i]) cyc.push_back(i);
	return cycle[i];
}

int find_grundy(int i) {
	if (grundy[i] != -1) return grundy[i];
	int mask = 0;
	for (int u: edge[i]) {
		mask |= (1 << find_grundy(u));
	}
	return grundy[i] = __builtin_ctz(~mask);
}

int grundy_single_init(int i) {
	int mask = 0;
	for (int u: edge[i]) {
		if (!cycle[u]) mask |= (1 << grundy[u]);
	}
	return mask;
}

int grundy_single(int i) {
	int mask = 0;
	for (int u: edge[i]) {
		mask |= (1 << grundy[u]);
	}
	return __builtin_ctz(~mask);
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	int n, t;
	cin >> n;

	edge.resize(n);
	memset(grundy, -1, sizeof(grundy));
	for (int i = 0; i < n; ++i) {
		cin >> t;
		t--;
		edge[t].push_back(i);
	}

	for (int i = 0; i < n; ++i) {
		if (!visited[i]) dfs(i);
	}

	for (int i = 0; i < n; ++i) {
		if (!cycle[i] && grundy[i] == -1) find_grundy(i);
	}

	int start = grundy_single_init(cyc[0]);
	int low = __builtin_ctz(~start);
	grundy[cyc[0]] = low;
	start |= (1 << low);
	for (int i = 1; i < cyc.size(); ++i) {
		grundy[cyc[i]] = grundy_single(cyc[i]);
	}
	if (grundy_single(cyc[0]) == grundy[cyc[0]]) {
		cout << "POSSIBLE";
		return 0;
	}
		
	grundy[cyc[0]] = __builtin_ctz(~start);
	for (int i = 1; i < cyc.size(); ++i) {
		grundy[cyc[i]] = grundy_single(cyc[i]);
	}
	if (grundy_single(cyc[0]) == grundy[cyc[0]]) {
		cout << "POSSIBLE";
	}
	else cout << "IMPOSSIBLE";
}
```