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.util.*;
public class Christmas {
	static ArrayList<ArrayList<Integer>> adj=new ArrayList<>();
	
	
	
	static void addEdge(ArrayList<ArrayList<Integer>>adj,int src,int dest) {
		adj.get(src).add(dest);
	}
	
	
	
	static void dfs(int curr,int par,int dp[]) {
		int leaf=0;
		if(adj.get(curr).size()>0) {
			for(int child:adj.get(curr)) {
				if(adj.get(child).size()==0) {
					leaf++;
				}
				else {
					dfs(child,curr,dp);
				}
			}
			if(leaf<3) {
				dp[curr]=1;
			}
		}
	}
	
	public static void main(String[] args) 
	{
		Scanner scan = new Scanner(System.in);
		
        int n = scan.nextInt();
		
		int[] dp = new int[n];
		
		for(int j=0;j<n;++j)
			adj.add(new ArrayList<Integer>());
		
		
		for(int i=1;i<n;++i)
		{
			int node = scan.nextInt();
			addEdge(adj,node-1,i);
		}
		
		
		dfs(0,0,dp);
		boolean spruce = true;
		for(int z: dp)
			if(z==1)
				spruce = false;
		
		if(spruce)
			System.out.println("Yes");
		else
			System.out.println("No");
	}

}