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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;

public class Christmas_Spruce {
	static 	ArrayList<Integer>[] nums;
	static boolean [] visited;
	public static void main(String[] args)throws Throwable {
		BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		int reps=Integer.parseInt(bf.readLine())-1;
		nums=new ArrayList[reps+2];
		visited=new boolean [reps+2]; 
		for(int i=0;i<nums.length;i++)
			nums[i]=new ArrayList<Integer>();
		int count=2;
		while(reps-->0)
		{
			int cur=Integer.parseInt(bf.readLine());
			nums[cur].add(count++);
		}
		System.out.println(dfs(1)? "Yes":"No");
	}
	static boolean dfs(int node)
	{
		visited[node]=true;
		if(nums[node].size()==0)
			return true;
		boolean ans=true;
		int count=0;
		for(int i=0;i<nums[node].size();i++)
		{
			if(nums[nums[node].get(i)].size()==0)
				count++;
			ans&=dfs(nums[node].get(i));
		}
		if(count!=0 && count>=3)
			return ans;
		return false;
	}
}