Problem:
Score : 200 points

Problem Statement

There are N rabbits, numbered 1 through N.

The i-th (1≤i≤N) rabbit likes rabbit a_i.
Note that no rabbit can like itself, that is, a_i≠i.

For a pair of rabbits i and j (i＜j), we call the pair (i，j) a friendly pair if the following condition is met.

Rabbit i likes rabbit j and rabbit j likes rabbit i.

Calculate the number of the friendly pairs.

Constraints

2≤N≤10^5

1≤a_i≤N

a_i≠i

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the number of the friendly pairs.

Sample Input 1

4
2 1 4 3

Sample Output 1

2

There are two friendly pairs: (1，2) and (3，4).

Sample Input 2

3
2 3 1

Sample Output 2

0

There are no friendly pairs.

Sample Input 3

5
5 5 5 5 1

Sample Output 3

1

There is one friendly pair: (1，5).

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
namespace Practice
{
	class Program
	{
		static void Main(string[] args)
		{
			Solve();
		}
		private const int MOD = 1000000007;
		static void Solve()
		{
			var n = ReadAndParseInt();
			var a = ReadAndParseIntArr();
			int ans = 0;
			for(int i=0;i<n;++i)
			{
				int idx = a[i] - 1;
				if(i == a[idx] - 1)
				{
					ans++;
				}
			}
			Console.WriteLine(ans / 2);
		}
		#region よく使う便利関数
		private static bool isPrime(long x)
		{
			if(x == 2) { return true; }
			if(x < 2 || x % 2 == 0) { return false; }
			long i = 3;
			while(i * i <= x)
			{
				if(x % i == 0) { return false; }
				i = i + 2;
			}
			return true;
		}
		private static long lcm(long x, long y)
		{
			return x / gcd(x, y) * y;
		}
		private static long gcd(long x, long y)
		{
			return y > 0 ? gcd(y, x % y) : x;
		}
		private static long pow(long x, long n)
		{
			if(n == 0) { return 1; }
			long res = pow(x * x % MOD, n / 2);
			if(n % 2 == 1)
			{
				res = res * x % MOD;
			}
			return res;
		}
		private static int ReadAndParseInt()
		{
			return int.Parse(Console.ReadLine());
		}
		private static int[] ReadAndParseIntArr()
		{
			return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
		}
		private static long ReadAndParseLong()
		{
			return long.Parse(Console.ReadLine());
		}
		private static long[] ReadAndParseLongArr()
		{
			return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
		}

		/// <summary>
		/// 指定した値以上の先頭のインデクスを返す
		/// </summary>
		/// <typeparam name="T">比較する値の型</typeparam>
		/// <param name="arr">対象の配列（※ソート済みであること）</param>
		/// <param name="start">開始インデクス [inclusive]</param>
		/// <param name="end">終了インデクス [exclusive]</param>
		/// <param name="value">検索する値</param>
		/// <param name="comparer">比較関数(インターフェイス)</param>
		/// <returns>指定した値以上の先頭のインデクス</returns>
		public static int LowerBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
		{
			int low = start;
			int high = end;
			int mid;
			while(low < high)
			{
				mid = ((high - low) >> 1) + low;
				if(comparer.Compare(arr[mid], value) < 0)
					low = mid + 1;
				else
					high = mid;
			}
			return low;
		}

		//引数省略のオーバーロード
		public static int LowerBound<T>(IReadOnlyList<T> arr, T value) where T : IComparable
		{
			return LowerBound(arr, 0, arr.Count, value, Comparer<T>.Default);
		}

		/// <summary>
		/// 指定した値より大きい先頭のインデクスを返す
		/// </summary>
		/// <typeparam name="T">比較する値の型</typeparam>
		/// <param name="arr">対象の配列（※ソート済みであること）</param>
		/// <param name="start">開始インデクス [inclusive]</param>
		/// <param name="end">終了インデクス [exclusive]</param>
		/// <param name="value">検索する値</param>
		/// <param name="comparer">比較関数(インターフェイス)</param>
		/// <returns>指定した値より大きい先頭のインデクス</returns>
		public static int UpperBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
		{
			int low = start;
			int high = end;
			int mid;
			while(low < high)
			{
				mid = ((high - low) >> 1) + low;
				if(comparer.Compare(arr[mid], value) <= 0)
					low = mid + 1;
				else
					high = mid;
			}
			return low;
		}

		//引数省略のオーバーロード
		public static int UpperBound<T>(IReadOnlyList<T> arr, T value)
		{
			return UpperBound(arr, 0, arr.Count, value, Comparer<T>.Default);
		}
		#endregion
	}
}