#include <cstdio>
#include <vector>
#include <algorithm>
int p[200001], N, d[200001], q[200001], D, vi[200001], sg[200001], cir[200001], L, w1[200001], w2[200001], w[200001];
std::vector < int > E[200001];
bool NiroBC(int start)
{
	w[1] = start;
	for (int i = 2; i <= L; i++)
		w[i] = w[i - 1] == w1[i] ? w2[i] : w1[i];
	return w[1] == (w[L] == w1[1] ? w2[1] : w1[1]);
}
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
	{
		scanf("%d", p + i);
		E[p[i]].push_back(i);
		d[p[i]]++;
	}
	for (int i = 1; i <= N; i++)
		if (!d[i])
			q[++D] = i;
	while (D)
	{
		int u = q[D--];
		for (int v : E[u])
			vi[sg[v]] = 1;
		while (vi[sg[u]])
			sg[u]++;
		for (int v : E[u])
			vi[sg[v]] = 0;
		if (!--d[p[u]])
			q[++D] = p[u];
	}
	for (int i = std::find(d + 1, d + N + 1, 1) - d; d[i] == 1; i = p[i])
		d[cir[++L] = i] = -1;
	for (int i = 1; i <= L; i++)
	{
		int u = cir[i];
		for (int v : E[u])
			if (d[v] != -1)
				vi[sg[v]] = 1;
		while (vi[w1[i]])
			w1[i]++;
		w2[i] = w1[i] + 1;
		while (vi[w2[i]])
			w2[i]++;
		for (int v : E[u])
			if (d[v] != -1)
				vi[sg[v]] = 0;
	}
	puts(NiroBC(w1[1]) || NiroBC(w2[1]) ? "POSSIBLE" : "IMPOSSIBLE");
	return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 <cstdio>
#include <vector>
#include <algorithm>
int p[200001], N, d[200001], q[200001], D, vi[200001], sg[200001], cir[200001], L, w1[200001], w2[200001], w[200001];
std::vector < int > E[200001];
bool NiroBC(int start)
{
	w[1] = start;
	for (int i = 2; i <= L; i++)
		w[i] = w[i - 1] == w1[i] ? w2[i] : w1[i];
	return w[1] == (w[L] == w1[1] ? w2[1] : w1[1]);
}
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
	{
		scanf("%d", p + i);
		E[p[i]].push_back(i);
		d[p[i]]++;
	}
	for (int i = 1; i <= N; i++)
		if (!d[i])
			q[++D] = i;
	while (D)
	{
		int u = q[D--];
		for (int v : E[u])
			vi[sg[v]] = 1;
		while (vi[sg[u]])
			sg[u]++;
		for (int v : E[u])
			vi[sg[v]] = 0;
		if (!--d[p[u]])
			q[++D] = p[u];
	}
	for (int i = std::find(d + 1, d + N + 1, 1) - d; d[i] == 1; i = p[i])
		d[cir[++L] = i] = -1;
	for (int i = 1; i <= L; i++)
	{
		int u = cir[i];
		for (int v : E[u])
			if (d[v] != -1)
				vi[sg[v]] = 1;
		while (vi[w1[i]])
			w1[i]++;
		w2[i] = w1[i] + 1;
		while (vi[w2[i]])
			w2[i]++;
		for (int v : E[u])
			if (d[v] != -1)
				vi[sg[v]] = 0;
	}
	puts(NiroBC(w1[1]) || NiroBC(w2[1]) ? "POSSIBLE" : "IMPOSSIBLE");
	return 0;
}

```