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:
// https://codeforces.com/problemset/problem/913/B
// rohchakr
//

import java.util.Scanner;

public class Main {
  public static void main (String [] args) {
    Scanner s = new Scanner (System.in);
    int n = s.nextInt();
    int [] parent = new int[n+1];
    for (int i =2; i<=n; i++) 
      parent[i] = s.nextInt();
    boolean [] isleaf = new boolean[n+1];
    for (int i =1; i<=n; i++)
      isleaf[i] = true;
    int [] leafChildrenCount = new int[n+1];
    for (int i =1; i<=n; i++)
      leafChildrenCount[i] = 0;

    // populate isleaf
    for (int i =2; i<=n; i++)
      isleaf[parent[i]] = false;

    // count leaf children
    for (int i =2; i<=n; i++)
      if (isleaf[i]) leafChildrenCount[parent[i]]++;

    boolean spruce = true;
    for(int i =1; i<=n; i++)
      if(isleaf[i] == false && leafChildrenCount[i] < 3) { spruce = false; break; }

    //for (int i =0;i<n+1;i++) System.out.println(isleaf[i]);
    //for (int i = 0; i<n+1; i++ ) System.out.println(leafChildrenCount[i]);
    System.out.println((spruce == true)?"Yes":"No");
  }
}