#include "bits/stdc++.h"
using namespace std;

const int maxn = 2e5 + 10;

int n;

vector<int> adj[maxn];

int used[maxn];

bool found;
vector<int> cicle, stk;

bool mrk[maxn];

void dfs(int v) {
    used[v] = 1;
    stk.push_back(v);

    for(auto u: adj[v])
	if(!used[u])
	    dfs(u);
	else
	    if(used[u] == 1) {
		found = true;

		for(int k = stk.size() - 1; k >= 0; --k) {
		    int c = stk[k];

		    cicle.push_back(c);
		    mrk[c] = true;

		    if(c == u)
			break;
		}
	    }

    stk.pop_back();
    used[v] = 2;
}

int g[maxn];

void dfsGrundy(int v) {
    set<int> Set;

    for(auto u: adj[v])
	if(!mrk[u]) {
	    dfsGrundy(u);
	    Set.insert(g[u]);
	}

    int k = 0;

    while(Set.find(k) != Set.end()) ++k;

    g[v] = k;
}

int G[maxn];

bool check() {
    int sz = cicle.size();

    for(int i = sz - 2; i >= 0; --i) {
	int c = cicle[i];
	int nx = cicle[i + 1];

	if(G[nx] != G[c])
	    continue;

	++G[c];
    }

    int First = cicle[0];
    int Last = cicle[sz - 1];

    if(G[First] == G[Last])
	return false;

    return true;
}

bool testCicle() {
    int sz = cicle.size();

    for(int i = 0; i < sz; ++i)
	G[cicle[i]] = g[cicle[i]];

    if(check())
	return true;

    for(int i = 0; i < sz; ++i)
	G[cicle[i]] = g[cicle[i]];

    ++G[cicle[sz - 1]];

    if(check())
	return true;

    return false;
}

bool solve() {
    for(int v = 1; v <= n; ++v)
	if(!used[v])
	    dfs(v);

    if(!found)
	return true;

    for(auto u: cicle)
	dfsGrundy(u);

    return testCicle();
}

int main() {
    scanf("%d", &n);

    for(int i = 1; i <= n; ++i) {
	int p;

	scanf("%d", &p);

	adj[p].push_back(i);
    }

    if(solve())
	printf("POSSIBLE\n");
    else
	printf("IMPOSSIBLE\n");

    return 0;
}

### Prompt

Please create a solution in cpp 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;

const int maxn = 2e5 + 10;

int n;

vector<int> adj[maxn];

int used[maxn];

bool found;
vector<int> cicle, stk;

bool mrk[maxn];

void dfs(int v) {
    used[v] = 1;
    stk.push_back(v);

    for(auto u: adj[v])
	if(!used[u])
	    dfs(u);
	else
	    if(used[u] == 1) {
		found = true;

		for(int k = stk.size() - 1; k >= 0; --k) {
		    int c = stk[k];

		    cicle.push_back(c);
		    mrk[c] = true;

		    if(c == u)
			break;
		}
	    }

    stk.pop_back();
    used[v] = 2;
}

int g[maxn];

void dfsGrundy(int v) {
    set<int> Set;

    for(auto u: adj[v])
	if(!mrk[u]) {
	    dfsGrundy(u);
	    Set.insert(g[u]);
	}

    int k = 0;

    while(Set.find(k) != Set.end()) ++k;

    g[v] = k;
}

int G[maxn];

bool check() {
    int sz = cicle.size();

    for(int i = sz - 2; i >= 0; --i) {
	int c = cicle[i];
	int nx = cicle[i + 1];

	if(G[nx] != G[c])
	    continue;

	++G[c];
    }

    int First = cicle[0];
    int Last = cicle[sz - 1];

    if(G[First] == G[Last])
	return false;

    return true;
}

bool testCicle() {
    int sz = cicle.size();

    for(int i = 0; i < sz; ++i)
	G[cicle[i]] = g[cicle[i]];

    if(check())
	return true;

    for(int i = 0; i < sz; ++i)
	G[cicle[i]] = g[cicle[i]];

    ++G[cicle[sz - 1]];

    if(check())
	return true;

    return false;
}

bool solve() {
    for(int v = 1; v <= n; ++v)
	if(!used[v])
	    dfs(v);

    if(!found)
	return true;

    for(auto u: cicle)
	dfsGrundy(u);

    return testCicle();
}

int main() {
    scanf("%d", &n);

    for(int i = 1; i <= n; ++i) {
	int p;

	scanf("%d", &p);

	adj[p].push_back(i);
    }

    if(solve())
	printf("POSSIBLE\n");
    else
	printf("IMPOSSIBLE\n");

    return 0;
}

```