Takahashi has N cards. The i-th of these cards has an integer A_i written on it.

Takahashi will choose an integer K, and then repeat the following operation some number of times:

* Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.)



For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation.

Constraints

* 1 \le N \le 3 \times 10^5
* 1 \le A_i \le N
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \ldots A_N


Output

Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t.

Examples

Input

3
2 1 2


Output

3
1
0


Input

5
1 2 3 4 5


Output

5
2
1
1
1


Input

4
1 3 3 3


Output

4
1
0
0
import java.util.*;
import java.util.Map.Entry;

import javax.swing.text.Segment;
import javax.xml.ws.WebEndpoint;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main //implements Runnable
{
//    static int dx[]={-1,0,1,0};
//    static int dy[]={0,-1,0,1};

    public static void main(String[] args)   throws Exception, IOException{        
        long mod=1000000007;
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        
        int n=sc.nextInt();
        PriorityQueue<Integer> q=new PriorityQueue<>();
        int d[]=new int[300001];
        int a[]=new int[n+1];
        for (int i = 0; i < n; i++) {
			d[sc.nextInt()]++;
		}
        ArrayList<Integer> l=new ArrayList<>();
        for (int i = 0; i < d.length; i++) {
			if(d[i]>0)l.add(d[i]);
		}
        sort(l);
        
        for (int i = 1,z=0,c=l.size()-1,s=n,x=n,v; i <= n; i++,x--) {
			while(-1<c && l.get(c)>x) {
				s-=l.get(c);
				c--;
				z++;
			}
			v=s+z*x;
			v/=x;
			a[x]=v;
		}
        int as[]=new int[n+1];
        db(a);
        for (int i = 1; i <=n ; i++) {
			as[a[i]]=i;
		}
        for (int i = n; 1<=i-1 ; i--) {
			if(as[i]!=0 && as[i-1]==0)as[i-1]=as[i];
		}
        for (int i = 1; i <=n ; i++) {
            out.println(as[i]);
		}
        

        out.println();
     	out.flush();
    }
    
    static void ret(String ans) {
    	System.out.println(ans);
    	System.exit(0);
    }
    
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
}


class P {
	int x, y, d;
	P(int  x, int y, int d) {
	  this.x=x;
	  this.y=y;
	  this.d=d;
	}
}

//class P implements Comparable<P>{
//    int a,b;
//    P(int a, int b) {
//    	this.b=b;
//    	this.a=a;
//    }
//
//    public int compareTo(P p){
//        return p.a-a;//des
//    }
//}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public int[] nextIntArray(int size) throws IOException{
        int r[] = new int[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextInt(); 
        }
        return r;
    }
    public long[] nextLongArray(int size) throws IOException{
        long r[] = new long[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextLong(); 
        }
        return r;
    }
    public char[] getCharSet() throws IOException{
        return this.nextString().toCharArray();
    }    
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}
