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.io.*;
    import java.lang.*;
    import java.math.*;
    public class B {
        public static void main(String[] args) throws Exception {
            BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
            // Scanner scan = new Scanner(System.in);
            PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
            int n = Integer.parseInt(bf.readLine());
            int[] parent = new int[n];
            int[] children = new int[n];
            for(int i=1; i<n; i++) {
              parent[i] = Integer.parseInt(bf.readLine())-1;
            }
            boolean[] isleaf = new boolean[n];
            Arrays.fill(isleaf, true);
            for(int i=0; i<n; i++) {
              isleaf[parent[i]] = false;
            }
            int[] leafcount = new int[n];
            for(int i=0; i<n; i++) {
              if(isleaf[i]) leafcount[parent[i]]++;
            }
            boolean answer = true;
            for(int i=0; i<n; i++) {
              if(isleaf[i]) continue;
              if(leafcount[i] >= 3) continue;
              answer = false;
            }
            if(answer) out.println("Yes");
            else out.println("No");
     
     
            // StringTokenizer st = new StringTokenizer(bf.readLine());
            // int n =  Integer.parseInt(st.nextToken());
     
     
            out.close(); System.exit(0);
        }
     
     
    }