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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace NotFounds
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Program().Solve(new ConsoleInput(Console.In, ' '));
            Console.Out.Flush();
        }

        public void Solve(ConsoleInput cin)
        {
            checked
            {
                var N = cin.ReadInt;
                var map = new HashMap<int, int>();
                for (int i = 0; i < N; ++i)
                    map[cin.ReadInt]++;
                var bad = map.Where(x => x.Key != x.Value);
                var a = bad.Where(x => x.Key > x.Value).Sum(x => x.Value);
                var b = bad.Where(x => x.Key < x.Value).Sum(x => x.Value - x.Key);
                WriteLine(a + b);
            }
        }
    }

    public class HashMap<K, V> : Dictionary<K, V>
    {
        public HashMap() : base() { }
        public HashMap(int cap) : base(cap) { }
        public HashMap(IDictionary<K, V> dictionary) : base(dictionary) { }
        new public V this[K i]
        {
            get
            {
                V v;
                return TryGetValue(i, out v) ? v : base[i] = default(V);
            }
            set { base[i] = value; }
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); }}
        public int ReadInt { get { return int.Parse(Read); }}
        public long ReadLong { get { return long.Parse(Read); }}
        public double ReadDouble { get { return double.Parse(Read); }}
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret;}
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret;}
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret;}
        public void ReadIntArrays(long N, out int[] A, out int[] B) { A = new int[N]; B = new int[N]; for (long i = 0; i < N; ++i) { A[i] = ReadInt; B[i] = ReadInt; }}
        public void ReadLongArrays(long N, out long[] A, out long[] B) { A = new long[N]; B = new long[N]; for (long i = 0; i < N; ++i) { A[i] = ReadLong; B[i] = ReadLong; }}
    }
}