1056_D. Decorate Apple Tree_5135
There is one apple tree in Arkady's garden. It can be represented as a set of junctions connected with branches so that there is only one way to reach any junctions from any other one using branches. The junctions are enumerated from 1 to n, the junction 1 is called the root.

A subtree of a junction v is a set of junctions u such that the path from u to the root must pass through v. Note that v itself is included in a subtree of v.

A leaf is such a junction that its subtree contains exactly one junction.

The New Year is coming, so Arkady wants to decorate the tree. He will put a light bulb of some color on each leaf junction and then count the number happy junctions. A happy junction is such a junction t that all light bulbs in the subtree of t have different colors.

Arkady is interested in the following question: for each k from 1 to n, what is the minimum number of different colors needed to make the number of happy junctions be greater than or equal to k?

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of junctions in the tree.

The second line contains n - 1 integers p_2, p_3, ..., p_n (1 ≤ p_i < i), where p_i means there is a branch between junctions i and p_i. It is guaranteed that this set of branches forms a tree.

Output

Output n integers. The i-th of them should be the minimum number of colors needed to make the number of happy junctions be at least i.

Examples

Input


3
1 1


Output


1 1 2 


Input


5
1 1 3 3


Output


1 1 1 2 3 

Note

In the first example for k = 1 and k = 2 we can use only one color: the junctions 2 and 3 will be happy. For k = 3 you have to put the bulbs of different colors to make all the junctions happy.

In the second example for k = 4 you can, for example, put the bulbs of color 1 in junctions 2 and 4, and a bulb of color 2 into junction 5. The happy junctions are the ones with indices 2, 3, 4 and 5 then.
import java.io.*; 
import java.math.*;
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.*; 
import java.util.StringTokenizer; 

public class Main 
{ 
    static int MAXN=201;
    static int spf[] = new int[MAXN]; 
    static int ans[]=new int[MAXN];
    static int id[]=new int[MAXN];
    static int sz[]=new int[MAXN];
    static HashSet s=new HashSet();
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 

		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 

		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} 
    static void sieves() 
    { 
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
            spf[i] = i; 
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
        for (long i=3; i*i<MAXN; i++) 
        { 
            if (spf[(int)i] == i) 
            { 
                for (long j=i*i; j<MAXN; j+=i) 
                    if (spf[(int)j]==j) 
                        spf[(int)j] = (int)i; 
            } 
        } 
    } 
    static void getFactorizations(int x) 
    { 
        Vector<Integer> ret = new Vector<>(); 
        HashSet w=new HashSet();
        while (x != 1 && spf[x]!=1) 
        { 
            if(!w.contains(spf[x]) && spf[x]!=1)
            {
            w.add(spf[x]);
            ans[spf[x]]++; 
            }
            x = x / spf[x]; 
        }
    } 
    static void dfs(int src,ArrayList<Integer>adj[],int dist[],int visit[]){
        visit[src]=1;
        for(int i:adj[src]){
            if(visit[i]==0){
                dfs(i,adj,dist,visit);
                //System.out.println(src+" "+i+" "+dist[src]+" "+dist[i]+" before");
                dist[src]+=dist[i];
                //System.out.println(src+" "+i+" "+dist[src]+" "+dist[i]+" after");
            }
        }
    }
	public static void main(String[] args) 
	{ 
		FastReader sc=new FastReader();
		int T=1;
		while(T-->0){
	        int N=sc.nextInt();
	        ArrayList<Integer>adj[]=new ArrayList[N];
	        for(int i=0;i<N;i++)
	        adj[i]=new ArrayList();
	        for(int i=0;i<N-1;i++){
	            int u=sc.nextInt()-1;
	            int v=(i+1);
	            adj[u].add(v);
	        }
	        int dist[]=new int[N];
	        int st=0;
	        for(int i=0;i<N;i++){
	            if(adj[i].size()==0)dist[i]=1;
	        }
	        int visit[]=new int[N];
	        dfs(st,adj,dist,visit);
	        Arrays.sort(dist);
	        for(int i=0;i<N;i++)
	        System.out.print(dist[i]+" ");
	        System.out.println();
		}
	}
	
	public static int root(int i)
    {
        while(i!=id[i])
        i=id[i];
        return i;
    }
    public static void union(int p,int q)
    {
        int i=root(p);
        int j=root(q);
        //System.out.println(i+" "+j);
        if(sz[i]<sz[j])
        {
            id[i]=j;
            sz[j]+=sz[i];
        }
        else
        {
            id[j]=i;
            sz[i]+=sz[j];
        }
        //max=Math.max(max,Math.max(sz[i],sz[j]));
    }
	public static void sieven(int n) 
    {
        boolean prime[] = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
        for(int p = 2; p*p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
                for(int i = p*2; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
        for(int p=2; p<=n;p++)
        if(prime[p]==true)
        s.add(p);
    } 
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    return gcd(b,a%b);
	}
	static long power(long x, long y, int p) 
    { 
        long res = 1;      
        x = x % p;  
        while (y > 0) 
        { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
    static class Pair
	{ 
		int x; 
		int y;
		public Pair(int x, int y) 
		{	 
			this.x = x; 
			this.y = y; 
		}	 
	} 
    static class Compare
	{ 
		static void compare(Pair arr[], int n) 
		{ 
			// Comparator to sort the pair according to second element 
			Arrays.sort(arr, new Comparator<Pair>() { 
				@Override public int compare(Pair p1, Pair p2) 
				{ 
					if(p1.x>p2.x)
					{
						return 1;
					}
					else if(p2.x>p1.x)
					{
						return -1;
					}
					else
					{
						return 0;
					} 
				} 
			}); 
		} 
	}
}
