Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

4
2 3 4 1

Sample Output 1

POSSIBLE

The assignment is possible: {a_i} = {0, 1, 0, 1} or {a_i} = {1, 0, 1, 0}.

Sample Input 2

3
2 3 1

Sample Output 2

IMPOSSIBLE

Sample Input 3

4
2 3 1 1

Sample Output 3

POSSIBLE

The assignment is possible: {a_i} = {2, 0, 1, 0}.

Sample Input 4

6
4 5 6 5 6 4

Sample Output 4

IMPOSSIBLE

Solution in PyPy2 (5.6.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

INF = 10 ** 18

N = input()
p = map(int, raw_input().split())
E = [[] for i in range(N + 1)]
for i in range(N):
    E[p[i]].append(i + 1)

flag = [True] * (N + 2)
grundy = [-1] * (N + 1)

def func(pos, pre, start):
    if grundy[pos] != -1:
        return grundy[pos]
    if pos == start and pre != -1:
        return INF
    ret = [func(to, pos, start) for to in E[pos]]
    if INF in ret:
        grundy[pos] = INF
        return INF
    for num in ret:
        flag[num] = False
    i = 0
    while True:
        if flag[i]:
            grundy[pos] = i
            val = i
            break
        i += 1
    for num in ret:
        flag[num] = True
    return val

grundy_ = []

def func2(pos):
    if grundy_[pos] != -1 and grundy_[pos] != INF:
        return grundy_[pos]
    ret = [func2(to) for to in E[pos]]
    for num in ret:
        flag[num] = False
    i = 0
    while True:
        if flag[i]:
            grundy_[pos] = i
            val = i
            break
        i += 1
    for num in ret:
        flag[num] = True
    return val

for i in range(N + 1):
    if grundy[i] == -1:
        ret = func(i, -1, i)
        if ret == INF:
            pos = i
            break

ff = [True] * (N + 2)
nex = 0
for to in E[pos]:
    if grundy[to] == INF:
        nex = to
    else:
        ff[grundy[to]] = False
cnt = 0
for i in range(N + 2):
    if ff[i]:
        grundy_ = list(grundy)
        grundy_[pos] = i
        func2(nex)
        #print grundy_
        if cnt == 0:
            pre = grundy_[pos]
            if grundy_[pos] != grundy_[nex]:
                print "POSSIBLE"
                exit()
        if cnt == 1:
            if grundy_[nex] == pre:
                print "POSSIBLE"
            else:
                print "IMPOSSIBLE"
            exit()
        cnt += 1