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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class trees {
	static ArrayList<Integer>adj[];
	static boolean vis[];
	static int c[];
	static int c2[];
	static void dfs(int u) {
		vis[u]=true;
		for(int v:adj[u]) {
			if(!vis[v]&&adj[v].size()==0)c[u]++;
			else c2[u]++;
			if(!vis[v]) 
				dfs(v);
			}
	}
	public static void main (String []args) throws IOException {
		 PrintWriter pw =new PrintWriter(System.out);
	Scanner sc=new Scanner(System.in);
	int n=sc.nextInt();
	adj=new ArrayList[n];
	vis=new boolean[n];
	c=new int[n];
	c2=new int[n];
	int f=0;
	for(int i=0;i<n;i++)adj[i]=new ArrayList<>();
	for( int i=0;i<n-1;i++) {
		int in=sc.nextInt()-1;if(i==0)f=in;
		adj[in].add(i+1);
	}
	dfs(f);
	
	boolean flag=true;
	for(int i=0;i<n;i++) {
		if((c[i]<3&&c[i]>0)||(c[i]<3&&c2[i]>0)) {
			flag=false;
			break;
		}
	}if(flag)pw.println("Yes");else pw.println("No");
	pw.flush();
	}
	static class Scanner {
		 
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}}
}