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.*;
import java.math.*;
import java.io.*;

public class CF_913B{
  public static void main(String[] args) throws IOException{
    FastScanner in = new FastScanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    int n = in.nextInt();
    
    int[] arr = new int[n];
    int[] copy = new int[n];
    int[] parent = new int[n];
    
    for( int i = 0; i < n - 1; i++ ){
      //set child and parent relations
      int num = in.nextInt();
      arr[--num]++; //increase child count (-1 because of indexing)
      copy[num]++;
      parent[i+1] = num;//set of parent (goes iteratively 2nd child onward) 
    }
    //deduct children count if total children count is > 0 (not a leaf)
    for ( int i = 1; i < n; i++ ) {
      if( copy[i] > 0 ) {
          arr[parent[i]]--;
      }
    }
    //if not a leaf and number of children is less than 3, then false
    boolean flag = true;
    for( int i = 0; i < n; i++ ){
      if( copy[i] != 0 && arr[i] < 3 ){
        flag = false; 
        break; 
      } 
    }
    if(flag) out.println("Yes");
    else out.println("No");
    out.close();
  }
  public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
			st = null;
		}
		public String next() throws IOException {
			while(st == null || !st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
	}
}