#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <set>

int main() {
	int n;
	std::cin >> n;

	std::vector<std::vector<int>> g(n);
	std::vector<std::vector<int>> h(n);
	std::vector<int> deg(n);
	for (int i = 0; i < n; i++) {
		int p;
		std::cin >> p;
		p--;
		g[p].push_back(i);
		h[i].push_back(p);
		deg[p]++;
	}

	std::queue<int> q;

	for (int i = 0; i < n; i++) {
		if (deg[i] == 0) {
			q.push(i);
		}
	}

	std::vector<int> ord(n, -1);
	std::vector<int> topo;
	int now = 0;
	while (!q.empty()) {
		int u = q.front();
		q.pop();
		ord[u] = now++;
		topo.push_back(u);

		for (int v : h[u]) {
			if (--deg[v] == 0) {
				q.push(v);
			}
		}
	}

	std::vector<int> dp(n);
	for (int u : topo) {
		std::set<int> mex;
		for (int v : g[u]) if (ord[v] != -1) {
			mex.insert(dp[v]);
		}
		while (mex.count(dp[u])) {
			dp[u]++;
		}
	}

	std::vector<int> cycle;
	for (int i = 0; i < n; i++) {
		if (ord[i] == -1) {
			int j = i;
			while (j != i || cycle.empty()) {
				cycle.push_back(j);
				for (int k : g[j]) if (ord[k] == -1) {
					j = k;
					break;
				}
			}
			break;
		}
	}

	if (cycle.empty()) {
		puts("POSSIBLE");
		return 0;
	}

	int f = cycle[0];
	std::vector<int> cand;
	std::set<int> st;
	for (int u : g[f]) {
		if (ord[u] != -1) {
			st.insert(dp[u]);
		}
	}

	int mex = 0;
	while (st.count(mex)) mex++;

	cand.push_back(mex);
	mex++;
	while (st.count(mex)) mex++;
	cand.push_back(mex);

	for (int c : cand) {
		dp[f] = c;

		for (int i = cycle.size() - 1; i >= 0; i--) {
			int u = cycle[i];
			std::set<int> st;
			for (int v : g[u]) {
				st.insert(dp[v]);
			}
			dp[u] = 0;
			while (st.count(dp[u])) dp[u]++;
		}
		if (dp[f] == c) {
			puts("POSSIBLE");
			return 0;
		}
	}
	puts("IMPOSSIBLE");
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 <algorithm>
#include <queue>
#include <set>

int main() {
	int n;
	std::cin >> n;

	std::vector<std::vector<int>> g(n);
	std::vector<std::vector<int>> h(n);
	std::vector<int> deg(n);
	for (int i = 0; i < n; i++) {
		int p;
		std::cin >> p;
		p--;
		g[p].push_back(i);
		h[i].push_back(p);
		deg[p]++;
	}

	std::queue<int> q;

	for (int i = 0; i < n; i++) {
		if (deg[i] == 0) {
			q.push(i);
		}
	}

	std::vector<int> ord(n, -1);
	std::vector<int> topo;
	int now = 0;
	while (!q.empty()) {
		int u = q.front();
		q.pop();
		ord[u] = now++;
		topo.push_back(u);

		for (int v : h[u]) {
			if (--deg[v] == 0) {
				q.push(v);
			}
		}
	}

	std::vector<int> dp(n);
	for (int u : topo) {
		std::set<int> mex;
		for (int v : g[u]) if (ord[v] != -1) {
			mex.insert(dp[v]);
		}
		while (mex.count(dp[u])) {
			dp[u]++;
		}
	}

	std::vector<int> cycle;
	for (int i = 0; i < n; i++) {
		if (ord[i] == -1) {
			int j = i;
			while (j != i || cycle.empty()) {
				cycle.push_back(j);
				for (int k : g[j]) if (ord[k] == -1) {
					j = k;
					break;
				}
			}
			break;
		}
	}

	if (cycle.empty()) {
		puts("POSSIBLE");
		return 0;
	}

	int f = cycle[0];
	std::vector<int> cand;
	std::set<int> st;
	for (int u : g[f]) {
		if (ord[u] != -1) {
			st.insert(dp[u]);
		}
	}

	int mex = 0;
	while (st.count(mex)) mex++;

	cand.push_back(mex);
	mex++;
	while (st.count(mex)) mex++;
	cand.push_back(mex);

	for (int c : cand) {
		dp[f] = c;

		for (int i = cycle.size() - 1; i >= 0; i--) {
			int u = cycle[i];
			std::set<int> st;
			for (int v : g[u]) {
				st.insert(dp[v]);
			}
			dp[u] = 0;
			while (st.count(dp[u])) dp[u]++;
		}
		if (dp[f] == c) {
			puts("POSSIBLE");
			return 0;
		}
	}
	puts("IMPOSSIBLE");
}
```