p03650 AtCoder Regular Contest 079 - Namori Grundy
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
```python
import sys
sys.setrecursionlimit(10**6)
n = int(input())
p = list(map(int, input().split()))
c = [[] for _ in range(n)]
is_leaf = [True for _ in range(n)]
for i in range(n):
	p[i] -= 1
	c[p[i]].append(i)
	is_leaf[p[i]] = False

if sum(is_leaf) == 0:
	if n%2 == 0:
		print("POSSIBLE")
	else:
		print("IMPOSSIBLE")
	sys.exit()

for i in range(n):
	if is_leaf[i]:
		cur = i
		break

visited_set = {cur}
visited_list = [cur]
while p[cur] not in visited_set:
	visited_list.append(p[cur])
	visited_set.add(p[cur])
	cur = p[cur]

root = p[cur]

grundy = [-1 for _ in range(n)]
g_set = [set() for _ in range(n)]

def dfs(x):
	res = 0
	for v in c[x]:
		dfs(v)
		g_set[x].add(grundy[v])
	while res in g_set[x]:
		res += 1
	grundy[x] = res
	return res

loop = [False for _ in range(n)]
loop[root] = True
ind = len(visited_list)-1
while visited_list[ind] != root:
	loop[visited_list[ind]] = True
	ind -= 1
#print(loop)

for i in range(n):
	if loop[i]:
		for x in c[i]:
			if not loop[x]:
				dfs(x)
				g_set[i].add(grundy[x])

cand = []
num = 0
while num in g_set[root]:
	num += 1
cand.append(num)
num += 1
while num in g_set[root]:
	num += 1
cand.append(num)

for x in cand:
	cur = root
	grundy[root] = x
	while True:
		num = 0
		while num in g_set[p[cur]] or num == grundy[cur]:
			num += 1
		grundy[p[cur]] = num
		if p[cur] == root:
			break
		cur = p[cur]
	if grundy[root] == x:
		#print(grundy)
		print("POSSIBLE")
		sys.exit()

print("IMPOSSIBLE")
```