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;
using System.Collections.Generic;
using System.Dynamic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Runtime.InteropServices;
using System.Runtime.InteropServices.ComTypes;
using System.Security;
using System.Text;
using static System.Console;
using static System.Math;
using  static Ex;
class Simple {
    void Solve() {
        //input
        var N = io.Int;
        var a = new int[N];
        N.REP(i=>a[i]=io.Int);
        
        //cal
        var dict = new Dictionary<int,int>();
        foreach(var n in a) {
            if(!dict.ContainsKey(n)) dict[n] = 0;
            dict[n]++;
        }
        var ans = dict.Aggregate(0, (acc, x) => {
            if      (x.Value <  x.Key) return acc + x.Value;
            else if (x.Value == x.Key) return acc;
            else                       return acc + (x.Value - x.Key); 
        });
        
        //ret
        WriteLine(ans);

    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    private void Stream() {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //SetIn(exStdIn);
        Solve();
        io.Flush();
    }
}
class SimpleIO {
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] {' ', '"', ','};
    StreamWriter sw = new StreamWriter(OpenStandardOutput()) {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public SimpleIO() {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        SetOut(sw);
    }
    string Next() {
        if(_bufferCnt < _nextBuffer.Length)
            return _nextBuffer[_bufferCnt++];
        var st = ReadLine();
        while(st == "")
            st = ReadLine();
        _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() => Out.Flush();
}
static class Ex {
    public static void REP(this int n, Action <int> act) {
        for(var i = 0; i < n; ++i)
            act(i);
    }
    public static void FOR(int a, int b, Action <int> act) {
        for(var i = a; i < b; ++i)
            act(i);
    }
}