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

public class H18B {
	public static void main(String[] args) throws NumberFormatException, IOException {
		
		BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(sc.readLine());
		
		boolean ans = true;
		
		ArrayList<Node> group = new ArrayList<Node>();
		for(int x=0; x<n+3; x++){
			group.add(new Node());
		}
		
		//System.out.print(group.get(0));
		
		for(int x=2; x<=n; x++){
			int p = Integer.parseInt(sc.readLine());
			
			group.get(p).addChild(x);
		}
		
		for(Node node: group){
			int leafCount = 0;
			if(!node.leaf){
				for(int y=0; y<node.children.size(); y++){
					if(group.get(node.children.get(y)).leaf){
						leafCount ++;
					}
				}
				
				if(leafCount < 3){
					ans = false;
					
					break;
				}
			}
		}
		
		if(ans){
			System.out.print("Yes");
		}
		else{
			System.out.print("No");
		}
	}
}

class Node {
	boolean leaf = true;
	ArrayList<Integer> children = new ArrayList<Integer>();
	
	
	public Node(){
		
	}
	
	public boolean addChild(int c){
		children.add(c);
		leaf = false;
		return leaf;
	}
}


/* 

BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));

int n = Integer.parseInt(sc.readLine());
String[] t = sc.readLine().split(" ");
int[] list = new int[n];
for(int x=0; x<n; x++){
	list[x] = Integer.parseInt(t[x]);
}
		
String[] dir = sc.readLine().split(" ");
int a = Integer.parseInt(dir[0]);
int b = Integer.parseInt(dir[1]);
int c = Integer.parseInt(dir[2]);
int d = Integer.parseInt(dir[3]);
int e = Integer.parseInt(dir[4]);

int n = Integer.parseInt(sc.readLine());

*/