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++14 (GCC 5.4.1) (judge verdict: Accepted)

//https://vjudge.net/contest/331523#problem/D
/*
* Author : MaxSally
*/
/********   All Required Header Files ********/
#include<bits/stdc++.h>
using namespace std;
/*******  All Required define Pre-Processors and typedef Constants *******/
#define SCD(t) scanf("%d",&t)
#define SCLD(t) scanf("%ld",&t)
#define SCLLD(t) scanf("%lld",&t)
#define SCC(t) scanf("%c",&t)
#define SCS(t) scanf("%s",t)
#define SCF(t) scanf("%f",&t)
#define SCLF(t) scanf("%lf",&t)
#define mem(a, b) memset(a, (b), sizeof(a))
#define rep(i, j, k) for (int i = j ; i <= k ; ++i)
#define rrep(i, j, k) for (int i = j; i >= k; --i)
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define foreach(i, a) for(auto i: a)
#define forEach(it, l) for (auto it = l.begin(); it != l.end(); it++)
#define in(A, B, C) assert( B <= A && A <= C)
#define mp make_pair
#define pb push_back
#define inf (int) (1e9 + 7)
#define epsi 1e-9
#define PI 3.1415926535897932384626433832795
#define mod 1000000007
#define read(type) readInt<type>()
#define io ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define ll long long int
#define left tuyiuoi
#define right fgjhk
#define ss second
#define ff first
#define debug(a) cout << #a << ": " << a << endl
#define debuga1(a, l, r) rep(i, l, r) cout << a[i] << " "; cout << endl
#define Flag(n) cout << "here " << n << endl
const double pi=acos(-1.0);
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> vll;
typedef pair<ll, ll> pll;
typedef vector<string> vs;
typedef vector<pii> vii;
typedef vector<pll> vpll;
typedef vector<vi> vvi;
typedef map<int,int> MPII;
typedef set<int> SETI;
typedef multiset<int> MSETI;
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int  uint64;

const int N = 100005;
MPII m;

int main(){
    io;
    //freopen("input.txt", "r", stdin);
    int n; cin >> n;
    rep(i, 1, n){
        int x; cin >> x;
        if(m.find(x) == m.end()){
            m.insert(mp(x, 1));
        }else{
            m[x]++;
        }
    }
    int total = 0;
    foreach(a, m){
        if(a.ff <= a.ss){
            total += a.ss - a.ff;
        }else{
            total += a.ss;
        }
    }
    cout << total;
    return 0;
}