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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        int n = sc.Int;
        var par = sc.IntArr.Select(x => x - 1).ToArray();
        var chld = new List<int>[n];
        for (int i = 0; i < n; i++)
        {
            chld[i] = new List<int>();
        }
        for (int i = 0; i < n; i++)
        {
            chld[par[i]].Add(i);
        }
        var visc = new int[n];
        int s = 0;
        while (true)
        {
            ++visc[s];
            if (visc[s] > 2) break;
            s = par[s];
        }
        var inloop = new bool[n];
        int ili = -1;
        for (int i = 0; i < n; i++)
        {
            inloop[i] = visc[i] > 1;
            if (ili == -1 && inloop[i]) {
                ili = i;
            }
        }
        var num = new int[n];
        for (int i = 0; i < n; i++)
        {
            num[i] = -1;
        }
        for (int i = 0; i < n; i++)
        {
            dfs(i, chld, inloop, num);
        }
        {
            int ss = ili;
            var nenum = new int[n];
            for (int i = 0; i < n; i++)
            {
                nenum[i] = num[i];
            }
            while (par[ss] != ili)
            {
                ss = par[ss];
                var lis = new List<int>();
                foreach (var item in chld[ss])
                {
                    lis.Add(nenum[item]);
                }
                lis.Sort();
                if (lis[0] != 0) {
                    nenum[ss] = 0;
                    continue;
                }
                for (int i = 0; i < lis.Count - 1; i++)
                {
                    if (lis[i] + 1 < lis[i + 1]) {
                        nenum[ss] = lis[i] + 1;
                        goto A;
                    }
                }
                nenum[ss] = lis[lis.Count - 1] + 1;
                A:
                continue;
            }
            {
                var lis = new List<int>();
                foreach (var item in chld[ili])
                {
                    lis.Add(nenum[item]);
                }
                lis.Sort();
                if (lis[0] != 0) {
                    if (nenum[ili] == 0) {
                        DBG("POSSIBLE");
                        return;
                    }
                }
                for (int i = 0; i < lis.Count - 1; i++)
                {
                    if (lis[i] + 1 < lis[i + 1]) {
                        if (nenum[ili] == lis[i] + 1) {
                            DBG("POSSIBLE");
                            return;
                        }
                    }
                }
                if (nenum[ili] == lis[lis.Count - 1] + 1) {
                    DBG("POSSIBLE");
                    return;
                }
            }
        }
        {
            int ss = ili;
            var nenum = new int[n];
            for (int i = 0; i < n; i++)
            {
                nenum[i] = num[i];
            }
            ++nenum[ili];
            while (par[ss] != ili)
            {
                ss = par[ss];
                var lis = new List<int>();
                foreach (var item in chld[ss])
                {
                    lis.Add(nenum[item]);
                }
                lis.Sort();
                if (lis[0] != 0) {
                    nenum[ss] = 0;
                    continue;
                }
                for (int i = 0; i < lis.Count - 1; i++)
                {
                    if (lis[i] + 1 < lis[i + 1]) {
                        nenum[ss] = lis[i] + 1;
                        goto A;
                    }
                }
                nenum[ss] = lis[lis.Count - 1] + 1;
                A:
                continue;
            }
            {
                var lis = new List<int>();
                foreach (var item in chld[ili])
                {
                    lis.Add(nenum[item]);
                }
                lis.Sort();
                if (lis[0] != 0) {
                    if (nenum[ili] == 0) {
                        DBG("POSSIBLE");
                        return;
                    }
                }
                for (int i = 0; i < lis.Count - 1; i++)
                {
                    if (lis[i] + 1 < lis[i + 1]) {
                        if (nenum[ili] == lis[i] + 1) {
                            DBG("POSSIBLE");
                            return;
                        }
                    }
                }
                if (nenum[ili] == lis[lis.Count - 1] + 1) {
                    DBG("POSSIBLE");
                    return;
                }
            }
        }
        Prt("IMPOSSIBLE");
        sw.Flush();
    }
    static int dfs(int p, List<int>[] chld, bool[] inloop, int[] num) {
        if (num[p] >= 0) return num[p];

        var lis = new List<int>();
        foreach (var item in chld[p])
        {
            if (!inloop[item]) {
                lis.Add(dfs(item, chld, inloop, num));
            }
        }
        if (lis.Count == 0) {
            return num[p] = 0;
        }
        lis.Sort();
        if (lis[0] != 0) {
            return num[p] = 0;
        }
        for (int i = 0; i < lis.Count - 1; i++)
        {
            if (lis[i] + 1 < lis[i + 1]) {
                return num[p] = lis[i] + 1;
            }
        }
        return num[p] = lis[lis.Count - 1] + 1;
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static void DBG(string a) { Console.WriteLine(a); }
    static void Prt(string a) { sw.WriteLine(a); }
    static void DBG<T>(IEnumerable<T> a) { DBG(string.Join(" ", a)); }
    static void DBG(params object[] a) { DBG(string.Join(" ", a)); }
    static void Prt<T>(IEnumerable<T> a) { Prt(string.Join(" ", a)); }
    static void Prt(params object[] a) { Prt(string.Join(" ", a)); }

    // for AOJ
    // static string Join<T>(string sep, IEnumerable<T> a) { return string.Join(sep, a.Select(x => x.ToString()).ToArray()); }
    // static void DBG<T>(IEnumerable<T> a) { DBG(Join(" ", a)); }
    // static void DBG(params object[] a) { DBG(Join(" ", a)); }
    // static void Prt<T>(IEnumerable<T> a) { Prt(Join(" ", a)); }
    // static void Prt(params object[] a) { Prt(Join(" ", a)); }
}
static class ex
{
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) { return Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile(); }
    public static Func<T, T> Lambda(Unary op) { return Expression.Lambda<Func<T, T>>(op(x), x).Compile(); }
}

class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    bool eq<T, U>() { return typeof(T).Equals(typeof(U)); }
    T ct<T, U>(U a) { return (T)Convert.ChangeType(a, typeof(T)); }
    T cv<T>(string s) { return eq<T, int>()    ? ct<T, int>(int.Parse(s))
                             : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                             : eq<T, double>() ? ct<T, double>(double.Parse(s))
                             : eq<T, char>()   ? ct<T, char>(s[0])
                                               : ct<T, string>(s); }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
    public void Multi<T, U, V, W, X, Y, Z>(out T a, out U b, out V c, out W d, out X e, out Y f, out Z g)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);  g = cv<Z>(ar[6]);}
}
class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n)
    {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static double[][] dE(int n)
    {
        var ret = new double[n][];
        for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double[][] pow(double[][] A, long n)
    {
        if (n == 0) return dE(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y)
    {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static double _dot(double[] x, double[] y)
    {
        int n = x.Length;
        double ret = 0, r = 0;
        for (int i = 0; i < n; i++)
        {
            double s = ret + (x[i] * y[i] + r);
            r = (x[i] * y[i] + r) - (s - ret);
            ret = s;
        }
        return ret;
    }
    public static long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static T[][] trans<T>(T[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double[][] A, double[] x)
    {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static double[][] mul(double[][] A, double[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b)
    {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) { return pow(a, Mod - 2); }
    public static long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y)
    {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    public static long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++)
        {
            int piv = denom[p - 1];
            if (piv > 1)
            {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
}