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 javafx.util.*;

public class Master {

    public static Scanner in = new Scanner(System.in);

    public static void main(String[] args) {
        int n = in.nextInt();
        Graph g = new Graph(n);
        for (int i = 2; i <= n; i++) {
            g.add(in.nextInt(), i);
        }
        ArrayList<Integer>[] data = g.data;
        boolean flg = true;
        boolean[] isLeaf = new boolean[n + 1];
        for (int i = 1; i <= n; i++) {
            if (data[i].size() == 1) {
                isLeaf[i] = true;
            }
        }
        for (int i = 1; i <= n; i++) {
            if (!isLeaf[i]) {
                int count = 0;
                ArrayList<Integer> adj = data[i];
                for (int val : adj) {
                    if (isLeaf[val]) {
                        count++;
                    }
                }
                if (count < 3) {
                    flg = false;
                    break;
                }
            }
        }
        if (flg) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }
    }

    public static class Graph {

        int V;
        ArrayList<Integer>[] data = null;

        public Graph(int v) {
            this.V = v + 1;

            data = new ArrayList[this.V];
            for (int i = 1; i <= v; i++) {
                data[i] = new ArrayList<Integer>();
            }

        }

        public void add(int u, int v) {
            data[u].add(v);
            data[v].add(u);
        }

    }
}