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

typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<ll,ll> pll;
typedef vector<bool> vb;
const ll oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define sz(c) ll((c).size())
#define all(c) begin(c), end(c)
#define FOR(i,a,b) for (ll i = (a); i < (b); i++)
#define FORD(i,a,b) for (ll i = (b)-1; i >= (a); i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define has(c,i) ((c).find(i) != end(c))
#define DBGDO(X) ({ if(1) cerr << "DBGDO: " << (#X) << " = " << (X) << endl; })

ll grundy(vvl &adj, vl &g, ll i) {
	ll res = 0;
	set<ll> s;
	for (ll j: adj[i]) s.insert(g[j]);
	while (has(s,res)) res++;
	return res;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	ll n; cin >> n;

	vvl adj(n);
	vl p(n);
	vl outdeg(n);

	FOR(i,0,n) {
		cin >> p[i];
		p[i]--;
		adj[p[i]].pb(i);
		outdeg[p[i]]++;
	}
	
	queue<ll> q;
	FOR(i,0,n) if (!outdeg[i]) q.push(i);
	
	vl g(n,-1);
	while (sz(q)) {
		ll i = q.front(); q.pop();
		g[i] = grundy(adj,g,i);
		if (!--outdeg[p[i]]) q.push(p[i]);
	}
	
	ll x = 0, y = -1;
	while (!outdeg[x]) x++;
	for (ll j: adj[x]) if (outdeg[j]) y = j;

	vl gg = g;

	g[x] = grundy(adj,g,x);
	for (ll i = p[x]; i != x; i = p[i]) g[i] = grundy(adj,g,i);

	if (g[x] != g[y]) {
		cout << "POSSIBLE" << endl;
		return 0;
	}
	
	g = gg;

	g[y] = grundy(adj,g,x);
	for (ll i = x; i != y; i = p[i]) g[i] = grundy(adj,g,i);

	if (grundy(adj,g,y) == g[y]) {
		cout << "POSSIBLE" << endl;
		return 0;
	}

	cout << "IMPOSSIBLE" << endl;
}


### 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;

typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<ll,ll> pll;
typedef vector<bool> vb;
const ll oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define sz(c) ll((c).size())
#define all(c) begin(c), end(c)
#define FOR(i,a,b) for (ll i = (a); i < (b); i++)
#define FORD(i,a,b) for (ll i = (b)-1; i >= (a); i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define has(c,i) ((c).find(i) != end(c))
#define DBGDO(X) ({ if(1) cerr << "DBGDO: " << (#X) << " = " << (X) << endl; })

ll grundy(vvl &adj, vl &g, ll i) {
	ll res = 0;
	set<ll> s;
	for (ll j: adj[i]) s.insert(g[j]);
	while (has(s,res)) res++;
	return res;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	ll n; cin >> n;

	vvl adj(n);
	vl p(n);
	vl outdeg(n);

	FOR(i,0,n) {
		cin >> p[i];
		p[i]--;
		adj[p[i]].pb(i);
		outdeg[p[i]]++;
	}
	
	queue<ll> q;
	FOR(i,0,n) if (!outdeg[i]) q.push(i);
	
	vl g(n,-1);
	while (sz(q)) {
		ll i = q.front(); q.pop();
		g[i] = grundy(adj,g,i);
		if (!--outdeg[p[i]]) q.push(p[i]);
	}
	
	ll x = 0, y = -1;
	while (!outdeg[x]) x++;
	for (ll j: adj[x]) if (outdeg[j]) y = j;

	vl gg = g;

	g[x] = grundy(adj,g,x);
	for (ll i = p[x]; i != x; i = p[i]) g[i] = grundy(adj,g,i);

	if (g[x] != g[y]) {
		cout << "POSSIBLE" << endl;
		return 0;
	}
	
	g = gg;

	g[y] = grundy(adj,g,x);
	for (ll i = x; i != y; i = p[i]) g[i] = grundy(adj,g,i);

	if (grundy(adj,g,y) == g[y]) {
		cout << "POSSIBLE" << endl;
		return 0;
	}

	cout << "IMPOSSIBLE" << endl;
}


```