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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.List;

public class b{

    static List<Integer>[] Edge;

    public static boolean dfs(int v){
        int cnt = 0;
        for(int u : Edge[v]){
            if(Edge[u].size() == 0)++cnt;
            else if(!dfs(u)){
                return false;
            }
        }
        return cnt>=3;
    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        Edge = new ArrayList[n+1];
        for(int i=1;i<=n;++i){
            Edge[i] = new ArrayList<>();
        }
        for(int i=0;i<n-1;++i){
            int p = scan.nextInt();
            Edge[p].add(i+2);
        }
        System.out.println((dfs(1) ? "Yes":"No"));
    }
}