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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using Number = System.Int32;

namespace Program {
	public class Solver {
		Random rnd = new Random();
		public void Solve() {
			var n = ri;
			var G = Enumerate(n, x => new List<int>());
			var par = new int[n];
			for (int i = 0; i < n; i++) {
				var u = ri - 1;
				G[u].Add(i);
				par[i] = u;
			}
			var g = new int[n];
			for (int i = 0; i < n; i++) g[i] = -1;
			var cnt = Enumerate(n, x => G[x].Count);
			var q = new Queue<int>();
			for (int i = 0; i < n; i++) if (cnt[i] == 0) q.Enqueue(i);
			while (q.Any()) {
				var p = q.Dequeue();
				cnt[par[p]]--;
				if (cnt[par[p]] == 0)
					q.Enqueue(par[p]);
				var s = new HashSet<int>();
				foreach (var t in G[p])
					s.Add(g[t]);
				for (int i = 0; i <= n; i++)
					if (s.Add(i)) { g[p] = i; break; }
			}
			var r = Enumerate(n, x => x).Where(x => g[x] == -1).First();
			Debug.WriteLine(par.AsJoinedString());
			Debug.WriteLine(g.AsJoinedString());
			Debug.WriteLine(r);
			Debug.WriteLine("------");
			for (int x = 0; x <= n; x++) {
				g[r] = x;
				for (var p = par[r]; ; p = par[p]) {
					var s = new HashSet<int>();
					foreach (var t in G[p])
						s.Add(g[t]);
					for (int i = 0; i <= n + 5; i++)
						if (s.Add(i)) {
							g[p] = i; break;
						}
					if (p == r) break;
				}
				if (g[r] == x) {
					Debug.WriteLine(g.AsJoinedString());
					Console.WriteLine("POSSIBLE");
					return;
				}
			}
			Console.WriteLine("IMPOSSIBLE");
		}

		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		int ri { get { return sc.Integer(); } }
		long rl { get { return sc.Long(); } }
		double rd { get { return sc.Double(); } }
		string rs { get { return sc.Scan(); } }
		public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n];
			for (int i = 0; i < a.Length; ++i) a[i] = f(i);
			return a;
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}
	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
		var solver = new Program.Solver();
		//* 
		var t = new System.Threading.Thread(solver.Solve, 50000000);
		t.Start();
		t.Join();
		//*/
		// solver.Solve();
		Console.Out.Flush();
	}
}
#endregion
#region Ex
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}

	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}
}

#endregion

#region Disjoint Set
/// <summary>
/// いくつかの要素を素集合に分割して保持するコレクションです．
/// </summary>
public class DisjointSet {
	int[] par;
	byte[] rank;
	/// <summary>
	/// 0 から <paramref name="N"/>-1 までの番号がついた <paramref name="N"/> 個の要素からなる集合を作成します．
	/// </summary>
	/// <param name="N">要素数</param>
	/// <remarks>このコンストラクタは O(N) で実行されます．</remarks>
	public DisjointSet(int N) {
		par = new int[N];
		rank = new byte[N];
		for (int i = 0; i < N; i++)
			par[i] = -1;
	}
	/// <summary>
	/// 指定した要素が属する集合の代表値を取得します．
	/// </summary>
	/// <param name="id">調べたい要素の 0-indexed での番号</param>
	/// <returns>指定した要素が属する集合の代表値</returns>
	/// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
	public int this[int id] {
		get {
			if ((par[id] < 0)) return id;
			return par[id] = this[par[id]];
		}
	}
	/// <summary>
	/// 指定した 2 つの要素が属する集合同士を 1 つに統合することを試みます．
	/// </summary>
	/// <param name="x">最初の要素の 0-indexed での番号</param>
	/// <param name="y">2 つ目の要素の 0-indexed での番号</param>
	/// <returns>統合に成功したならば true，そうでなければ false．</returns>
	/// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
	public bool Unite(int x, int y) {
		x = this[x]; y = this[y];
		if (x == y) return false;
		if (rank[x] < rank[y]) { var tmp = x; x = y; y = tmp; }
		par[x] += par[y];
		par[y] = x;
		if (rank[x] == rank[y])
			rank[x]++;
		return true;
	}
	/// <summary>
	/// 指定した要素が属する集合のサイズを取得します．
	/// </summary>
	/// <param name="x">指定する要素の 0-indexed での番号</param>
	/// <returns>集合のサイズ</returns>
	/// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
	public int Size(int x) { return -par[this[x]]; }

	/// <summary>
	/// 指定した 2 つの要素が属する集合が同じかどうかを判定する．計算量 O(α(N))．
	/// </summary>
	/// <param name="x">最初の要素の 0-indexed での番号</param>
	/// <param name="y">2 つ目の要素の 0-indexed での番号</param>
	/// <returns>同じならば true，そうでなければ false．</returns>
	/// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
	public bool Same(int x, int y) { return this[x] == this[y]; }

}
#endregion