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

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

    static class TaskB {
        ArrayList<Integer>[] a;

        public void solve(int testNumber, FReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] p = new int[n + 1];
            a = new ArrayList[n + 1];

            for(int i = 1; i <= n; ++i)
                a[i] = new ArrayList<>();

            for(int i = 1; i < n; ++i) {
                p[i + 1] = in.nextInt();
                a[p[i + 1]].add(i + 1);
            }

            out.println(dfs(1) ? "Yes" : "No");
        }

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

    }

    static class FReader {
        private BufferedReader  r;
        private String          line;
        private StringTokenizer st;
        private String          token;

        public FReader() {
            this(System.in);
        }

        public FReader(InputStream i) {
            r = new BufferedReader(new InputStreamReader(i));
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        private String peekToken() {
            if(token == null)
                try {
                    while(st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if(line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch(IOException e) { }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}