#include<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
int n,pre[N],deg[N],q[N],size,vis[N],C,ans[N];
vector<int> e[N];
bool test(int x){
	q[size=1]=x;
	for (int i=1;i<=size;i++){
		int v=q[i];
		C++;
		for (int j=0;j<e[v].size();j++) vis[ans[e[v][j]]]=C;
		while (vis[ans[v]]==C) ans[v]++;
		if (!--deg[pre[v]]) q[++size]=pre[v];
	}
	for (int i=1;i<=n;i++){
		C++;
		for (int j=0;j<e[i].size();j++) vis[ans[e[i][j]]]=C;
		int Ans=0;
		while (vis[Ans]==C) Ans++;
		if (Ans!=ans[i]) return 0;
	}
	return 1;
}
int circle;
void find_cir(int x){
	static int vis[N],C;C++;
	while (!vis[x]) vis[x]=C,x=pre[x];
	if (vis[x]==C) circle=x;
}
int Deg[N],Ans[N];
void work(){
	for (int i=1;i<=n;i++) find_cir(i);
	int x=circle;
	for (int i=1;i<=n;i++) Deg[i]=deg[i],Ans[i]=ans[i];
	C++;
	for (int i=0;i<e[x].size();i++) if (!deg[e[x][i]]) vis[ans[e[x][i]]]=C;
	while (vis[ans[x]]==C) ans[x]++;
	deg[pre[x]]--;deg[x]--;
	if (test(pre[x])) return;
	for (int i=1;i<=n;i++) deg[i]=Deg[i],ans[i]=Ans[i];
	C++;
	for (int i=0;i<e[x].size();i++) if (!deg[e[x][i]]) vis[ans[e[x][i]]]=C;
	while (vis[ans[x]]==C) ans[x]++;
	for (ans[x]++;vis[ans[x]]==C;ans[x]++);
	deg[pre[x]]--;deg[x]--;
	if (!test(pre[x])) puts("IMPOSSIBLE"),exit(0);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&pre[i]),e[pre[i]].push_back(i);
	for (int i=1;i<=n;i++) deg[i]=e[i].size();
	for (int i=1;i<=n;i++) if (!deg[i]) q[++size]=i;
	for (int i=1;i<=size;i++){
		int v=q[i];
		C++;
		for (int j=0;j<e[v].size();j++) vis[ans[e[v][j]]]=C;
		while (vis[ans[v]]==C) ans[v]++;
		if (!--deg[pre[v]]) q[++size]=pre[v];
	}
	if (size!=n) work();
	puts("POSSIBLE");
	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<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
int n,pre[N],deg[N],q[N],size,vis[N],C,ans[N];
vector<int> e[N];
bool test(int x){
	q[size=1]=x;
	for (int i=1;i<=size;i++){
		int v=q[i];
		C++;
		for (int j=0;j<e[v].size();j++) vis[ans[e[v][j]]]=C;
		while (vis[ans[v]]==C) ans[v]++;
		if (!--deg[pre[v]]) q[++size]=pre[v];
	}
	for (int i=1;i<=n;i++){
		C++;
		for (int j=0;j<e[i].size();j++) vis[ans[e[i][j]]]=C;
		int Ans=0;
		while (vis[Ans]==C) Ans++;
		if (Ans!=ans[i]) return 0;
	}
	return 1;
}
int circle;
void find_cir(int x){
	static int vis[N],C;C++;
	while (!vis[x]) vis[x]=C,x=pre[x];
	if (vis[x]==C) circle=x;
}
int Deg[N],Ans[N];
void work(){
	for (int i=1;i<=n;i++) find_cir(i);
	int x=circle;
	for (int i=1;i<=n;i++) Deg[i]=deg[i],Ans[i]=ans[i];
	C++;
	for (int i=0;i<e[x].size();i++) if (!deg[e[x][i]]) vis[ans[e[x][i]]]=C;
	while (vis[ans[x]]==C) ans[x]++;
	deg[pre[x]]--;deg[x]--;
	if (test(pre[x])) return;
	for (int i=1;i<=n;i++) deg[i]=Deg[i],ans[i]=Ans[i];
	C++;
	for (int i=0;i<e[x].size();i++) if (!deg[e[x][i]]) vis[ans[e[x][i]]]=C;
	while (vis[ans[x]]==C) ans[x]++;
	for (ans[x]++;vis[ans[x]]==C;ans[x]++);
	deg[pre[x]]--;deg[x]--;
	if (!test(pre[x])) puts("IMPOSSIBLE"),exit(0);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&pre[i]),e[pre[i]].push_back(i);
	for (int i=1;i<=n;i++) deg[i]=e[i].size();
	for (int i=1;i<=n;i++) if (!deg[i]) q[++size]=i;
	for (int i=1;i<=size;i++){
		int v=q[i];
		C++;
		for (int j=0;j<e[v].size();j++) vis[ans[e[v][j]]]=C;
		while (vis[ans[v]]==C) ans[v]++;
		if (!--deg[pre[v]]) q[++size]=pre[v];
	}
	if (size!=n) work();
	puts("POSSIBLE");
	return 0;
}
```