Problem:
Score : 300 points

Problem Statement

You are given a sequence of positive integers of length N, a = (a_1, a_2, ..., a_N).
Your objective is to remove some of the elements in a so that a will be a good sequence.

Here, an sequence b is a good sequence when the following condition holds true:

For each element x in b, the value x occurs exactly x times in b.

For example, (3, 3, 3), (4, 2, 4, 1, 4, 2, 4) and () (an empty sequence) are good sequences, while (3, 3, 3, 3) and (2, 4, 1, 4, 2) are not.

Find the minimum number of elements that needs to be removed so that a will be a good sequence.

Constraints

1 \leq N \leq 10^5

a_i is an integer.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of elements that needs to be removed so that a will be a good sequence.

Sample Input 1

4
3 3 3 3

Sample Output 1

1

We can, for example, remove one occurrence of 3. Then, (3, 3, 3) is a good sequence.

Sample Input 2

5
2 4 1 4 2

Sample Output 2

2

We can, for example, remove two occurrences of 4. Then, (2, 1, 2) is a good sequence.

Sample Input 3

6
1 2 2 3 3 3

Sample Output 3

0

Sample Input 4

1
1000000000

Sample Output 4

1

Remove one occurrence of 10^9. Then, () is a good sequence.

Sample Input 5

8
2 7 1 8 2 8 1 8

Sample Output 5

5

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

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{

    static class Program
    {
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            //

            int N = GetInt();
            var A = GetIntArray();

            Dictionary<int, int> dic = new Dictionary<int, int>();
            for(int i = 0; i < N; i++)
            {
                var temp = A[i];
                if (dic.ContainsKey(temp)) { dic[temp]++; }
                else { dic.Add(temp, 1); }
            }
            var ans = 0;
            foreach(var d in dic)
            {
                if (d.Value > d.Key) ans += d.Value - d.Key;
                else if (d.Value < d.Key) ans += d.Value;
            }

            Console.WriteLine(ans);

            //
            Console.Out.Flush();
            Console.ReadKey();
        }

        static void Solve()
        {

        }

        static long GCD(long a, long b) { return b != 0 ? GCD(b, a % b) : a; }


        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public int GetInt() { return int.Parse(Console.ReadLine()); }
        static public long GetLong() { return long.Parse(Console.ReadLine()); }
        static public string[] GetStrArray() { return Console.ReadLine().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Split(' ').Select(char.Parse).ToArray(); }
        static public List<double> GetDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }
        static public void WriteObjects<T>(IEnumerable<T> values) { foreach (var o in values) { Console.Write(o + " "); } }
        static string yesno(this bool b) { return b ? "yes" : "no"; }
        static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        static string YESNO(this bool b) { return b ? "YES" : "NO"; }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => 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);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c, out V d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<V>(ar[3]);
        }
    }
}