#if 0
date +%Y.%m.%d

题解先咕着。
#endif
#include <cstdio>
#include <set>
#define debug(...) fprintf(stderr, __VA_ARGS__)

typedef long long ll;

struct {
	inline operator int () { int x; return scanf("%d", &x), x; }
	inline operator ll () { ll x; return scanf("%lld", &x), x; }
	template<class T> inline void operator () (T &x) { x = *this; }
	template<class T, class ...A> inline void operator () (T &x, A &...a)
	{ x = *this; this -> operator ()(a...); }
} read;

const int maxn = 200005;
int p[maxn];
int deg[maxn];
int mex[maxn];
int stack[maxn], sp;
std::set<int> set[maxn];

int main() {
	int n = read;
	for(int i = 1; i <= n; i ++)
		++ deg[p[i] = read];

	for(int i = 1; i <= n; i ++)
		if(!deg[i])
			stack[++ sp] = i;

	while(sp) {
		int x = stack[sp --];

		while(set[x].count(mex[x]))
			++ mex[x];

		set[p[x]].insert(mex[x]);

		-- deg[p[x]];
		if(!deg[p[x]])
			stack[++ sp] = p[x];
	}

	int tot = 0;
	for(int i = 1; i <= n; i ++)
		if(deg[i]) {
			while(set[i].count(mex[i]))
				++ mex[i];
			/* debug("%d : %d\n", i, mex[i]); */
			++ tot;
			set[0].insert(mex[i]);
		}

	if((tot & 1) and set[0].size() == 1) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
}

### 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
#if 0
date +%Y.%m.%d

题解先咕着。
#endif
#include <cstdio>
#include <set>
#define debug(...) fprintf(stderr, __VA_ARGS__)

typedef long long ll;

struct {
	inline operator int () { int x; return scanf("%d", &x), x; }
	inline operator ll () { ll x; return scanf("%lld", &x), x; }
	template<class T> inline void operator () (T &x) { x = *this; }
	template<class T, class ...A> inline void operator () (T &x, A &...a)
	{ x = *this; this -> operator ()(a...); }
} read;

const int maxn = 200005;
int p[maxn];
int deg[maxn];
int mex[maxn];
int stack[maxn], sp;
std::set<int> set[maxn];

int main() {
	int n = read;
	for(int i = 1; i <= n; i ++)
		++ deg[p[i] = read];

	for(int i = 1; i <= n; i ++)
		if(!deg[i])
			stack[++ sp] = i;

	while(sp) {
		int x = stack[sp --];

		while(set[x].count(mex[x]))
			++ mex[x];

		set[p[x]].insert(mex[x]);

		-- deg[p[x]];
		if(!deg[p[x]])
			stack[++ sp] = p[x];
	}

	int tot = 0;
	for(int i = 1; i <= n; i ++)
		if(deg[i]) {
			while(set[i].count(mex[i]))
				++ mex[i];
			/* debug("%d : %d\n", i, mex[i]); */
			++ tot;
			set[0].insert(mex[i]);
		}

	if((tot & 1) and set[0].size() == 1) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
}

```