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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //var N = line1[0];
            //var M = line1[1];
            //var a = new long[M];
            //var b = new long[M];

            //int bridge = 0;

            //int[,] dag = new int[N,N];

            //for (int i = 0; i < M; i++)
            //{
            //    var line2 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //    a[i] = line2[0]-1;
            //    b[i] = line2[1]-1;
            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}

            //for (int i = 0; i < M; i++)
            //{
            //    bool[] visited = new bool[N];
            //    dag[a[i], b[i]] = 0;
            //    dag[b[i], a[i]] = 0;
            //    DFS(0,visited,dag);

            //    if (visited.Where(n => n == true).Count() != N)
            //    {
            //        bridge++;
            //    }

            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}
            //Console.WriteLine(bridge);
            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);

            //var A = line1[0];
            //var B = line1[1];
            //var C = line1[2];
            //var D = line1[3];
            //var E = line1[4];
            //var F = line1[5];

            //var N = int.Parse(Console.ReadLine());
            //char[] mozi = new char[N];
            //long[] MARCH = new long[5];
            //long cnt = 0;


            //for (int i = 0; i < N; i++)
            //{
            //    mozi[i] = Console.ReadLine().ToCharArray()[0];
            //}

            //MARCH[0] = mozi.Where(n => n == 'M').Count();
            //MARCH[1] = mozi.Where(n => n == 'A').Count();
            //MARCH[2] = mozi.Where(n => n == 'R').Count();
            //MARCH[3] = mozi.Where(n => n == 'C').Count();
            //MARCH[4] = mozi.Where(n => n == 'H').Count();

            //for (int i = 0; i < 3; i++)
            //{
            //    for (int j = i + 1; j < 4; j++)
            //    {
            //        for (int k = j + 1; k < 5; k++)
            //        {
            //            cnt += MARCH[i] * MARCH[j] * MARCH[k];
            //        }
            //    }
            //}

            //Console.WriteLine(cnt);

            //var N = int.Parse(Console.ReadLine());

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //var line2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //int candy = 0;
            //int MAX = 0;

            //for (int i = 0; i < N; i++)
            //{
            //    for (int k = 0; k <= i; k++)
            //    {
            //        candy += line1[k];
            //    }

            //    for (int j = N - 1; j >= i; j--)
            //    {
            //        candy += line2[j];
            //    }

            //    MAX = Math.Max(candy,MAX);
            //    candy = 0;
            //}

            //Console.WriteLine(MAX);

            //var N = int.Parse(Console.ReadLine());
            //List<int[]> list = new List<int[]>();
            //int t = 0;
            //int x = 0;
            //int y = 0;

            //for (int i = 0; i < N; i++)
            //{
            //    var txy = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //    list.Add(txy);
            //}

            //foreach (var item in list)
            //{
            //    if (item[0] - t >= Math.Abs(item[1] + item[2] - x - y))
            //    {

            //        if (((item[0] - t) % 2 == 1 && Math.Abs(x + y - item[1] - item[2]) % 2 == 1) ||
            //            ((item[0] - t) % 2 == 0 && Math.Abs(x + y - item[1] - item[2]) % 2 == 0))
            //        {
            //            t = item[0];
            //            x = item[1];
            //            y = item[2];
            //        }
            //        else
            //        {
            //            Console.WriteLine("No");
            //            return;
            //        }
            //    }
            //    else
            //    {
            //        Console.WriteLine("No");
            //        return;
            //    }
            //}

            //Console.WriteLine("Yes");

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

            //if (line1[1] >= 10000)
            //{
            //    for (int i = 0; i <= line1[1]/10000; i++)
            //    {
            //        for (int j = 0; j <= line1[1] / 5000; j++)
            //        {
            //            if (10000 * i + 5000 * j + (line1[0] - i - j) * 1000 == line1[1] && line1[0] - i - j >= 0)
            //            {
            //                Console.WriteLine("{0} {1} {2}",i,j,line1[0] - i - j);
            //                return;
            //            }
            //        }
            //    }
            //}
            //else
            //{
            //    for (int i = 0; i < 2; i++)
            //    {
            //        for (int j = 0; j <= 9; j++)
            //        {
            //            if (5000 * i + 1000 * j == line1[1] && i + j == line1[0])
            //            {
            //                Console.WriteLine("{0} {1} {2}", 0, i, j);
            //                return;
            //            }
            //        }
            //    }
            //}

            //Console.WriteLine("{0} {1} {2}", -1, -1, -1);


            //var N = int.Parse(Console.ReadLine());
            //int[,] station = new int[N,3];
            //long sum = 0;


            //for (int i = 0; i < N - 1; i++)
            //{
            //    var line = Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
            //    station[i, 0] = line[0];
            //    station[i, 1] = line[1];
            //    station[i, 2] = line[2];
            //}

            //for (int j = 0; j < N -1; j++)
            //{
            //    for (int i = j; i < N - 1; i++)
            //    {
            //        var F = station[i, 2];
            //        var S = station[i, 1];
            //        if (i == j)
            //        {
            //            sum += station[i, 0] + station[i, 1];
            //        }
            //        else
            //        {
            //            if (sum < S)
            //            {
            //                sum = S + station[i, 0];
            //            }
            //            else if (sum % F == 0)
            //            {
            //                sum += station[i, 0];
            //            }
            //            else
            //            {
            //                sum += F - (sum % F) + station[i, 0];
            //            }
            //        }
            //    }

            //    Console.WriteLine(sum);
            //    sum = 0;
            //}
            //Console.WriteLine(sum);

            //var line = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //long A = line[0];
            //int i = 0;

            //while (A <= line[1])
            //{
            //    A *=2;
            //    i++;
            //}

            //Console.WriteLine(i);
            var N = long.Parse(Console.ReadLine());
            var line = Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
            Dictionary<long, long> dic = new Dictionary<long, long>();
            long sum = 0;

            for (int i = 0; i < N; i++)
            {
                if (dic.ContainsKey(line[i]))
                {
                    dic[line[i]]++;
                }
                else
                {
                    dic.Add(line[i], 1);
                }
            }

            foreach (var item in dic)
            {
                if (item.Key == item.Value)
                {

                }
                else if (item.Key < item.Value)
                {
                    sum += item.Value - item.Key;
                }
                else
                {
                    sum += item.Value;
                }
            }

            Console.WriteLine(sum);
        }

        public static void DFS(int v,bool[] visited,int[,] dag)
        {
            visited[v] = true;

            for (int i = 0; i < visited.Length; i++)
            {
                if (dag[v, i] == 0) continue;
                if (visited[i]) continue;
                DFS(i,visited,dag);
            }

        }

        public static long LowerBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long 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 long LowerBound<T>(T[] arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }

        public static long UpperBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long 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 long UpperBound<T>(T[] arr, T value)
        {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
    }

}