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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class ChristmasSpruce {

    public static void main(String[] args) {
        Scanner scanner = new Scanner();

        int n = scanner.nextInt();
        boolean isSpruce = true;
        List<List<Integer>> edges = new ArrayList<>();

        for(int i=0; i<n; i++)
            edges.add(new ArrayList<>());

        for(int v=2; v<=n; v++) {
            int parent = scanner.nextInt()-1;
            edges.get(parent).add(v);
        }

        for(int i=0; i<edges.size(); i++) {
            int vertexEdges = edges.get(i).size();
            if(vertexEdges > 0 && vertexEdges < 3) {
                isSpruce = false;
                break;

            } else if (vertexEdges >= 3) {
                List<Integer> neighbours = edges.get(i);
                int leafCount = 0;

                for(int j=0; j<neighbours.size(); j++) {
                    if(edges.get(neighbours.get(j)-1).size() == 0)
                        leafCount++;
                }

                if(leafCount < 3) {
                    isSpruce = false;
                    break;
                }
            }

        }

        if(isSpruce)
            System.out.println("Yes");
        else
            System.out.println("No");
    }

    private static class Scanner {
        private BufferedReader br;
        private StringTokenizer st;

        Scanner() { br = new BufferedReader(new InputStreamReader(System.in)); }

        String next() {
            if(st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }

        long nextLong() { return Long.parseLong(next()); }

        double nextDouble() { return Double.parseDouble(next()); }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}