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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
public class codeforces {

    public static boolean bata(ArrayList<Integer>[] tree,boolean[] vis,boolean[] isleaf,int n){
        for(int i=1;i<=n;i++){
            if(tree[i].size()>1){
                int c=0;
                for(int x:tree[i]){
                    if(isleaf[x])
                    c++;
                    else
                    if(!vis[x]){
                        vis[x]=true;
                        if(tree[x].size()==1)
                        {
                            isleaf[x]=true;
                            c++;
                        }
                    }
                }
                if(c<3)
                return false;
            }
        }
        return true;
    }

    static class pair{
        int x;
        int y;

        public pair(int x,int y){
            this.x=x;
            this.y=y;
        }
    }

    public static long power(int a,int b){
        if(a==0 || b==0)
        return 1;
        long ans=power(a,b/2);
        ans*=ans;
        if(b%2==1)
        ans*=a;
        return ans;
    }

    public static long max(long a,long b){
        return Math.max(a,b);
    }
    public static void main(String args[] ) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        // StringBuilder str=new StringBuilder();
        PrintWriter out=new PrintWriter(System.out);
        int n=Integer.parseInt(br.readLine());
        // String[] l=br.readLine().split(" ");
        ArrayList<Integer>[] tree=new ArrayList[n+1];
        boolean[] vis=new boolean[n+1];
        boolean[] isleaf=new boolean[n+1];
        for(int i=1;i<=n;i++)
        tree[i]=new ArrayList<>();
        for(int i=0;i<n-1;i++){
            int t=Integer.parseInt(br.readLine());
            tree[t].add(i+2);
            tree[i+2].add(t);
        }
        // for(int i=1;i<=n;i++){
        //     out.print(i+" --> ");
        //     for(int node:tree[i])
        //     out.print(node+" ");
        //     out.println();
        // }
        out.println(bata(tree,vis,isleaf,n)?"Yes":"No");
        // out.println(sum);
        out.close();
   }
}