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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {
	static long	sum	= 0;
	static int	n;
	static Boolean [][]visited  ;
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();

	}

	static class TaskC {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt() ; 
			Vertix[] tree = new Vertix[n]; 
			HashMap<Integer,Vertix> h = new HashMap<Integer,Vertix>() ; 
			for (int i = 0; i < n; i++)
			{
				tree[i]=new Vertix((i+1)) ;
				h.put((i+1), tree[i]) ;
			}
			for (int i = 1; i < n; i++)
			{
				int x = in.nextInt() ;
				h.get(x).children.add(h.get((i+1)));
				h.get(i+1).parent  =h.get(x);			
			}
			boolean f  =true ;

			for (int i = 0; i < tree.length; i++)
			{
				int c=0;
				if(!isLeaf(tree[i]))
				{
					c=0;
					for (int j = 0; j < tree[i].children.size(); j++)
						if(isLeaf(tree[i].children.get(j)))
							c++;
					if(c<3)
						f= false ;
				}

			}
			if(f)
				System.out.println("Yes");
			else
				System.out.println("No");



		}

		public boolean isLeaf(Vertix root)
		{

			if(root.parent!=null && root.children.size()==0)
				return true ;
			else
				return false;
		}



		int  binarySearch(int arr[], int l, int r, int x)   /// begin by 0 and n-1
		{
			if (r>=l)
			{
				int mid = l + (r - l)/2;
				if (arr[mid] == x)
					return mid;
				if (arr[mid] > x)
					return binarySearch(arr, l, mid-1, x);
				return binarySearch(arr, mid+1, r, x);
			}
			return -1;
		}
		static int CeilIndex(int A[], int l, int r, int key)    //// start by l=-1, r=n
		{
			while (r - l > 1)
			{
				int m = l + (r - l)/2;
				if (A[m]>=key)
					r = m;
				else
					l = m;
			}

			return r;
		}




	}


	static class InputReader {
		public BufferedReader	reader;
		public StringTokenizer	tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e)
				{
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

	}
	static class Vertix{
		int x ; 
		ArrayList<Vertix> children; 
		Vertix parent; 

		public Vertix(int x){
			this.x = x ;
			this.children= new ArrayList<Vertix>();
		}

	}

	static class Pair implements Comparable<Pair> {
		int x ; 
		int y ; 

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

		}

		@Override
		public int compareTo(Pair p) {
			if (this.x < p.x)
				return -1;
			else if (this.x > p.x)
				return 1;
			else
				return 0;

		}
		//
	}

}