Problem: Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex u is called a child of vertex v and vertex v is called a parent of vertex u if there exists a directed edge from v to u. A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found [here](https://goo.gl/1dqvzz).

Input

The first line contains one integer n — the number of vertices in the tree (3 ≤ n ≤ 1 000). Each of the next n - 1 lines contains one integer pi (1 ≤ i ≤ n - 1) — the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ i).

Vertex 1 is the root. It's guaranteed that the root has at least 2 children.

Output

Print "Yes" if the tree is a spruce and "No" otherwise.

Examples

Input

4
1
1
1


Output

Yes


Input

7
1
1
1
2
2
2


Output

No


Input

8
1
1
1
1
3
3
3


Output

Yes

Note

The first example:

<image>

The second example:

<image>

It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.text.DecimalFormat;
import java.util.*;

public class Solution
{
    public static void main(String[] args)
    {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        //--------Solution-------------------------------------------------------//
        int n = sc.nextInt();
        int[] a = new int[n+1];
        int[] p = new int[n+1];
        boolean[] l = new boolean[n+1];
        for(int i=2;i<=n;i++) l[i]=true;

        for(int i=2;i<=n;i++){
            p[i] = sc.nextInt();
        }

        for(int i=2;i<=n;i++){
            a[p[i]]++;
            if(l[p[i]]){l[p[i]]=false; a[p[p[i]]]--;}
        }

        boolean ans=true;
        for(int i=1;i<n;i++){
            //out.println(a[i]);
            if(!l[i] && a[i]<3) {ans=false; break;}
        }

        if(ans) out.println("Yes");
        else out.println("No");
        //-----------------------------------------------------------------------//

        out.close();
    }

    //-----------Helper Functions------------------------------------------------//
    static int[] readIntArray(MyScanner sc,int n){
        int[] a = new int[n];
        for(int i=0;i<n;i++) a[i]= sc.nextInt();
        return a;
    }

    static long[] readLongArray(MyScanner sc,int n){
        long[] a = new long[n];
        for(int i=0;i<n;i++) a[i]=sc.nextLong();
        return a;
    }

    static void printIntArray(PrintWriter out,int[] a){
        for(int i:a) out.print(i+" ");
        out.println();
    }

    static boolean nextPermutation(int[] a){
        int i = a.length - 1;
        while(i>0 && a[i-1]>=a[i]) i--;

        if(i==0) return false;

        int j = a.length - 1;
        while(a[j]<=a[i-1]) j--;

        int temp = a[i-1];
        a[i-1]=a[j];
        a[j]=temp;

        j = a.length - 1;
        while(i<j){
            temp = a[i];
            a[i] = a[j];
            a[j] = temp;
            i++; j--;
        }
        return true;
    }

    static long max_subarray(long[] a){
        long lmax = a[0], gmax=a[0];

        for(int i=1; i<a.length; i++){
            lmax = Math.max(a[i],lmax+a[i]);
            gmax = Math.max(lmax,gmax);
        }
        return gmax;
    }

    //-----------PrintWriter for faster output-----------------------------------//
    public static PrintWriter out;

    //-----------MyScanner class for faster input--------------------------------//
    public static class MyScanner
    {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(){
            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;
        }

    }
}


//-----------------------Helper Classes------------------------------------------//
class Pair implements Comparable<Pair>
{
    int first;
    int second;

    Pair(int f,int s){
        first=f;
        second=s;
    }

    public int compareTo(Pair p){
        return this.first - p.first;
    }
}