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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            List<int> lstS = new List<int>();                                   // 該当Xの個数一覧
            for (int i = 0; i <= iN; i++) { lstS.Add(0); }                      // 前もって箱準備   X 0始まり
            int iDelCnt = 0;                                                    // 削除回数
            sS = Console.ReadLine().Trim().Split(' ');
            for (int i = 0; i < sS.Length; i++)
            {
                int iTmp = int.Parse(sS[i]);
                if (iTmp < iN) { lstS[iTmp] += 1; }                             // iNより大きいと意味ない
                else { iDelCnt += 1; }                                          // 削除回数加算
            }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            for (int i = 1; i < lstS.Count; i++)
            {
                if (lstS[i] != 0)
                {
                    if (lstS[i] == i) { }                                       // X がi個あればOK
                    else if (lstS[i] > i) { iDelCnt += lstS[i] - i; }           // X がiより多ければiになるまで削除
                    else { iDelCnt += lstS[i]; }                                // X がiより少なければ全部削除
                }
            }

            // 出力
            Console.WriteLine("{0}", iDelCnt.ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }
}