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.HashMap;
import java.util.ArrayList;

public class cf_Christmas_Spruce {
	static ArrayList<ArrayList<Integer>> g;
	static StringBuilder answer;
	static int[] c;
	static HashMap<Integer,Integer> map=new HashMap<>();
	public static void main(String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		Integer t=1;
		answer=new StringBuilder();
		while(t-->0) {
			int n=Integer.parseInt(br.readLine().trim());
			g=new ArrayList<>();
			for(int i=0;i<=n;i++) {
				g.add(new ArrayList<>());
			}
			c=new int[n+1];
			int i=1;
			while(n-->1) {
				int p=Integer.parseInt(br.readLine().trim());
				map.put(p,1);
				g.get(p).add((++i));
			}
			call(1,0);
			int count=0;
			for(int x:c) {
				count+=x>=3?1:0;
//				System.out.print(x+" ");
			}
			System.out.println(count==map.size()?"YES":"NO");
		}
		
	}
	static void call(int curr,int par) {
		if(g.get(curr).size()==0) {
			c[par]++;
		}
		else {
			for(int child:g.get(curr)) {
				call(child,curr);
			}
		}
	}
	
}