#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
const int MN = 200200;
int dp[MN];
vvi g;
bitset<MN> bs,sv,vs,sc;
vi ord,st;
bool found;
int ds(int u) {
	if(dp[u] != -1) return dp[u];
	vi ok;ok.push_back(MN+2);
	for(int i=0;i<g[u].size();i++) {
		int v = g[u][i];
		if(sc[u] && sc[v]) {continue;}
		ok.push_back(ds(v));
	}
	sort(ok.begin(),ok.end());
	int res = 0;
	while(ok[res] == res) {res++;}
	return dp[u] = res;
}
void cyc(int u) {
	st.push_back(u);
	sv.set(u);
	vs.set(u);
	for(int i=0;i<g[u].size();i++) {
		if(found) return;
		int v = g[u][i];
		if(sv[v]) {
			found = true;
			while(1) {
				ord.push_back(st.back());
				sc.set(st.back());
				if(st.back() == v) break;
				st.pop_back();
			}
			return;
		} else {
			if(!vs[v]) {
			cyc(v);
			}
		}
	}
	if(found) return;
	sv.reset(u);
	st.pop_back();
}
int n;
void calc() {
	found = false;
	for(int i=0;i<n;i++) {
		if(!vs[i]) {
			cyc(i);
		}
	}
}
int main() {
	memset(dp,-1,sizeof(dp));
	scanf("%d",&n);
	g.assign(n,vi());
	for(int i=0;i<n;i++) {
		int a;
		scanf("%d",&a);
		a--;
		g[a].push_back(i);
	}
	calc();
	int rep = ord[0];
	bool sm = true;
	for(int i=0;i<ord.size();i++) {
		if(ds(rep) != ds(ord[i])) {
			sm = false;break;
		}
	}
	bool poss = (!sm) || (ord.size()%2 == 0);
	printf("%sPOSSIBLE\n",poss?"":"IM");
}
### 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 <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
const int MN = 200200;
int dp[MN];
vvi g;
bitset<MN> bs,sv,vs,sc;
vi ord,st;
bool found;
int ds(int u) {
	if(dp[u] != -1) return dp[u];
	vi ok;ok.push_back(MN+2);
	for(int i=0;i<g[u].size();i++) {
		int v = g[u][i];
		if(sc[u] && sc[v]) {continue;}
		ok.push_back(ds(v));
	}
	sort(ok.begin(),ok.end());
	int res = 0;
	while(ok[res] == res) {res++;}
	return dp[u] = res;
}
void cyc(int u) {
	st.push_back(u);
	sv.set(u);
	vs.set(u);
	for(int i=0;i<g[u].size();i++) {
		if(found) return;
		int v = g[u][i];
		if(sv[v]) {
			found = true;
			while(1) {
				ord.push_back(st.back());
				sc.set(st.back());
				if(st.back() == v) break;
				st.pop_back();
			}
			return;
		} else {
			if(!vs[v]) {
			cyc(v);
			}
		}
	}
	if(found) return;
	sv.reset(u);
	st.pop_back();
}
int n;
void calc() {
	found = false;
	for(int i=0;i<n;i++) {
		if(!vs[i]) {
			cyc(i);
		}
	}
}
int main() {
	memset(dp,-1,sizeof(dp));
	scanf("%d",&n);
	g.assign(n,vi());
	for(int i=0;i<n;i++) {
		int a;
		scanf("%d",&a);
		a--;
		g[a].push_back(i);
	}
	calc();
	int rep = ord[0];
	bool sm = true;
	for(int i=0;i<ord.size();i++) {
		if(ds(rep) != ds(ord[i])) {
			sm = false;break;
		}
	}
	bool poss = (!sm) || (ord.size()%2 == 0);
	printf("%sPOSSIBLE\n",poss?"":"IM");
}
```