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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.DataInputStream;
import java.util.Iterator;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Read in = new Read(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, Read in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<Integer> a[] = (ArrayList<Integer>[]) new ArrayList[n + 1];
            for (int i = 0; i < n + 1; i++) {
                a[i] = new ArrayList<Integer>();
            }
            for (int i = 1; i < n; i++) {
                a[in.nextInt()].add(i + 1);
            }
            boolean v[] = new boolean[n + 1];
            if (dfs(a, v, 1)) {
                out.println("Yes");
            } else {
                out.println("No");
            }
        }

        static boolean dfs(ArrayList<Integer>[] a, boolean[] v, int i) {
            v[i] = true;
            Iterator<Integer> it = a[i].iterator();
            int ct = 0;
            while (it.hasNext()) {
                int tm = it.next();
                if (a[tm].size() == 0) {
                    ct++;
                    v[tm] = true;
                } else if (!dfs(a, v, tm)) {
                    return false;
                }
            }
            if (ct > 2) {
                return true;
            }
            return false;
        }

    }

    static class Read {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public Read(InputStream inputStream) {
            din = new DataInputStream(inputStream);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Read(String file_name) {
            try {
                din = new DataInputStream(new FileInputStream(file_name));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public int nextInt() {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() {
            try {
                bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

    }
}