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.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

public class Task {

    static class Vertex {

        ArrayList<Vertex> child = new ArrayList<>();
        int num;

        public Vertex(int num) { this.num = num; }

        boolean isLeaf() {
            return child.size() == 0;
        }

        boolean dfs() {
            int childCount = 0;
            for (Vertex v : child) {
                if (v.isLeaf()) childCount++;
            }
            return childCount >= 3;
        }
    }

    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        HashMap<Integer, Vertex> map = new HashMap<>();
        for (int i = 0; i < n - 1; i++) {
            int cur = in.nextInt();
            Vertex v = map.getOrDefault(cur, new Vertex(cur));
            map.put(i + 2, map.getOrDefault(i + 2, new Vertex(i + 2)));
            v.child.add(map.get(i + 2));
            map.put(cur, v);
        }
        boolean ans = false;
        for (Vertex v : map.values()) {
            if (!v.isLeaf())
                if (!v.dfs())
                    ans = true;
        }
        if (ans) out.println("No");
        else out.println("Yes");
        out.close();
    }
}